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Full text of "Physics_For_Entertaiment"

TRANSLATED FROM THE RUSSIAN BY 
A. SHKAROVSKY 

DESIGNED BY L. L A M M 



CONTENTS 

From thr Authors Foreword to the 13th Edition 9 

Chapter One 
SPEED AND VELOCITY. COMPOSITION OF MOTIONS 

HOW FAST 1)0 WE MOVE? !3 

RACING AGAINST TIME 16 

THE THOUSANDTH OF A SECOM) 17 

THE SLOW-MOTION CAMERA 20 

WHEN WE MOVE ROUND THE SUN FASTER 21 

THE CART-WHEEL RIDDLE 22 

THE WHEEL'S SLOWEST PART 1!4 

BRAIN-TEASER 24 

WHERE DID THE YACHT CAST OFF? r> 

Chapter Two 
GRAVITY AND WEIGHT. LEVERS. PRESSURE 

TRY TO STAND UP! 28 

WALKING AND RUNNING 30 

HOW TO JUMP FROM A MOVING CAR . . . 3,1 

CATCHING A BULLET 35 

MELON AS BOMB 35 

HOW TO WEIGH YOURSELF 38 

WHERE ARE THINGS HEAVIER? 38 

HOW MUCH DOES A FALLING BODY WEIGH? 40 

FROM EARTH TO MOON 41 

FLYING TO THE MOON: JULES VERNE VS. THE 

TRUTH 44 



FAULTY SCALES CAN GIVE RIGHT WEIGHT . 46 

STRONGER THAN YOU THINK 47 

WHY DO SHARP THINGS PRICK? 48 

-COMFORTABLE BED ... OF ROCK 49 

Chapter Three 
ATMOSPHERIC RESISTANCE 

BULLET AND AIR 51 

BIG BERTHA 52 

WHY DOES A KITE FLY? 53 

LIVE GLIDERS 54 

BALLOONING SEEDS 55 

DELAYED PARACHUTE JUMPING 56 

THE BOOMERANG 57 

Chapter Four 
ROTATION. "PERPETUAL MOTION" MACHINES 

HOW TO TELL A BOILED AND RAW EGG APART? 60 

WHIRLIGIG 61 

INKY WHIRLWINDS 62 

THE DELUDED PLANT 63 

"PERPETUAL MOTION" MACHINES 64 

"THE SNAG" 67 

"IT'S THEM BALLS THAT DO IT" 68 

UFIMTSEV'S ACCUMULATOR 70 

"A MIRACLE, YET NOT A MIRACLE" 70 

MORE "PERPETUAL MOTION "MACHINES ... 72 

THE "PERPETUAL MOTION" MACHINE PETER 

THE GREAT WANTED TO BUY 73 



Chapter Five 
PROPERTIES OF LIQUIDS AND GASES 

THE TWO COFFEE-POTS 77 

IGNORANCE OF ANCIENTS 77 

LIQUIDS PRESS ... UPWARDS 79 

WHICH IS HEAVIER? .80 

A LIQUID'S NATURAL SHAPK 81 

WHY IS SHOT ROUND? 81* 

THE "BOTTOMLESS" WINEGLASS . . . .84 

UNPLEASANT PROPERTY 85 

THE UNSINKABLE COIN .87 

CARRYING WATER IN A SIEVE .... 88 

FOAM HELPS ENGINEERS 81) 

FAKE "PERPETUAL MOTION" MACHINE . . . 90 

BLOWING SOAP BUBBLES .92 

THINNEST OF ALL <),> 

WITHOUT WETTING A FINGKH 97 

HOW WE DRINK 98 

A BETTER FUNNEL 98 

A TON OF WOOD AND A TON OF IRON .... 99 

THE MAN WHO WEIGHED NOTHING 99 

"PERPETUAL" CLOCK 10* 

Chapter Six 
HEAT 

WHEN IS THE OKTYABRSKAYA RAILWAY LONG- 

ER? 106 

UNPUNISHED THEFT 107 

HOW HIGH IS THE EIFFEL TOWEH? .... 108 

FROM TEA GLASS TO WATER GAUGE .... 109 

THE BOOT IN THE BATHHOUSE 110 



HOW TO WORK MIRACLES Ill 

SELF-WINDING CLOCK 113 

INSTRUCTIVE CIGARETTE 115 

ICE THAT DOESN'T MELT IN BOILING WATER 115 

ON TOP OR BENEATH? 116 

DRAUGHT FROM CLOSED WINDOW 117 

MYSTERIOUS TWIRL 117 

DOES A WINTER COAT WARM YOU? 118 

THE SEASON UNDERFOOT 119 

PAPER POT 120 

WHY IS ICE SLIPPERY? 122 

THE ICICLES PROBLEM 123 

Chapter Seven 
LIGHT 

TRAPPED SHADOWS 126 

THE CHICK IN THE EGG 128 

PHOTOGRAPHIC CARICATURES 128 

THE SUNRISE PROBLEM 130 

Chapter Eight 
REFLECTION AND REFRACTION 

SEEING THROUGH WALLS 132 

THE SPEAKING HEAD 134 

IN FRONT OR BEHIND 135 

IS A MIRROR VISIBLE? 135 

IN THE LOOKING-GLASS 135 

MIRROR DRAWING 137 

SHORTEST AND FASTEST 138 

AS THE CROW FLIES . 139 



THE KALEIDOSCOPE 140 

PALACES OF ILLUSIONS AND MIRAGES .... 141 

WHY LIGHT REFRACTS AND HOW 144 

LONGER WAY FASTER 145 

THE NEW CRUSOES 148 

ICE HELPS TO LIGHT FIRE 150 

HELPING SUNLIGHT 152 

MIRAGES 154 

"THE GREEN RAY" 15K 

Chapter Nine 

VISION 

BEFORE PHOTOGRAPHY WAS INVENTED . . . 1(51 

WHAT MANY DON'T KNOW HOW TO DO ... 1G2 

HOW TO LOOK AT PHOTOGRAPHS 163 

HOW FAR TO HOLD A PHOTOGRAPH . . . 101 

QUEER EFFECT OF MAGNIFYING GLASS . . . 165 

ENLARGED PHOTOGRAPHS 1GH 

BEST SEAT IN MOVIE-HOUSE 167 

FOR READERS OF PICTORIAL MAGAZINKS . 108 

HOW TO LOOK AT PAINTINGS 160 

THREE DIMENSIONS IN TWO 170 

STEREOSCOPE 170 

BINOCULAR VISION 172 

WITH ONE EYE AND TWO 176 

DETECTING FORGERY 176 

AS GIANTS SEE IT 177 

UNIVERSE IN STEREOSCOPE 179 

THREE-EYED VISION 180 

STEREOSCOPIC SPARKLE 181 

TRAIN WINDOW OBSERVATION 182 



THROUGH TINTED EYEGLASSES 183 

"SHADOW MARVELS" 184 

MAGIC METAMORPHOSES 185 

HOW TALL IS THIS BOOK? 186 

TOWER CLOCK DIAL 187 

BLACK AND WHITE 187 

WHICH IS BLACKER? 189 

STARING PORTRAIT 190 

MORE OPTICAL ILLUSIONS 191 

SHORT-SIGHTED VISION 195 

Chapter Ten 
SOUND AND HEARING 

HUNTING THE ECHO J<)7 

SOUND AS RULER 199 

SOUND MIRRORS 200 

SOUND IN THEATRE 202 

SEA-BOTTOM ECHO 202 

WHY DO BEES BUZZ? 204 

AUDITORY ILLUSIONS 205 

WHERE'S THE GRASSHOPPER? 205 

THE TRICKS OUR EARS PLAY 207 

99 QUESTIONS 208 



FROM THE AUTHOR'S FOREWORD 
TO THE 13th EDITION 

The aim of this book is not so much to give you some fresh knowl- 
edge, as to help you "learn what you already know". In other words, 
my idea is to brush up and liven your basic knowledge of physics, and 
to teach you how to apply it in various ways. To achieve this purpose 
conundrums, brain-teasers, entertaining anecdotes and stories, amusing 
experiments, paradoxes and unexpected comparisons all dealing 
with physics and based on our everyday world and sci-fic are afford- 
ed. Believing sci-fic most appropriate in a book of this kind, I have 
quoted extensively from Jules Verne, H. G. Wells, Mark Twain and 
other writers, because, besides providing entertainment, the fantastic 
experiments these writers describe may well serve as instructive illus- 
trations at physics classes. 

I have tried my best both to arouse interest and to amuse, as I be- 
lieve that the greater the interest one shows, the closer the heed one 
pays and the easier it is to grasp the meaning thus making for better 
knowledge. 

However, I have dared to defy the customary methods employed in 
writing books of this nature. Hence, you will find very little in the way 
of parlour tricks or spectacular experiments. My purpose is different, 
being mainly to make you think along scientific lines from the angle 
of physics, and amass associations with the variety of things from every- 
day life. I have tried in rewriting the original copy to follow the prin- 
ciple that was formulated by Lenin thus: "The popular writer leads his 
reader towards profound thoughts, towards profound study, proceeding 
from simple and generally known facts; with the aid of simple argu- 



merits or striking examples he shows the main conclusions to be drawn 
from those facts and arouses in the mind of the thinking reader ever 
newer questions. The popular writer does not presuppose a reader that 
docs not think, that cannot or does not wish to think; on the con- 
trary, he assumes in the undeveloped reader a serious intention to use 
his head and aids him in his serious and difficult work, leads him, helps 
him over his first steps, and teaches him to go forward independently. 
(Collected Works, Vol. 5, p. 311, Moscow 1961.) 

Since so much interest has been shown in the history of this book, 
let me give you a few salient points of its "biography". 

Physics for Entertainment first appeared a quarter of a century ago, 
being the author's first-born in his present large family of several score 
of such books. So far, this bookwhich is in two partshas been pub- 
lished in Russian in a total print of 200,000 copies. Considering that 
many are to be found on the shelves of public libraries, where each copy 
reaches dozens of readers, I daresay that millions have read it. I have 
received letters from readers in the furthermost corners of the Soviet 
Union. 

A Ukrainian translation was published in 1925, and German and 
Yiddish translations in 1931. A condensed German translation was 
published in Germany. Excerpts from the book have been printed 
in French in Switzerland and Belgium and also in Hebrew in 
Palestine. 

Its popularity, which attests to the keen public interest displayed 
in physics, has obliged me to pay particular note to its standard, which 
explains the many changes and additions in reprints. In all the 25 
years it has been in existence the book has undergone constant revision, 
its latest edition having barely half of the maiden copy and practically 
not a single illustration from the first edition. 

Some have asked me to refrain from revision, not to be compelled "to 
buy the new revised edition for the sake of a dozen or so new pages". 
Scarcely can such considerations absolve me of my obligation constantly 
to improve this book in every way. After all Physics for Enter- 
tainment is not a work of fiction. It is a book on science be it even 
popular science and the subject taken, physics, is enriched even in 

10 



its fundamentals with every day. This must necessarily be taken into 
consideration. 

On the other hand, I have been reproached more than once for fail- 
ing to deal in this book with questions such as the latest achievements 
in radio engineering, nuclear fission, modern theories and the like. 
This springs from a misunderstanding. This book has a definite pur- 
pose; it is the task of other books to deal \\ilh the points mentioned. 

Physics for Entertainment has, besides its second part, some other 
associated books of mine. One, Physics at Every Step, is intended for 
the unprepared layman who has still not embarked upon a systematic 
study of physics. The other two are, on the contrary, for people >\ho 
have gone through a secondary school course in physics. These arc 
Mechanics for Entertainment and Do You Know Your Physics?, the 
Jast being the sequel, as it wore, to this book. 

1936 Y. P er elm an 



CHAPTER ONE 

SPEED AND VELOCITY. COMPOSITION 
OF MOTIONS 



HOW FAST DO WE MOVE? 

A good athlete can run 1.5 km in about 3 min 50 pec the 1958 
world record was 3 min 36.8 sec. Any ordinary person usually does, 
when walking, about 1.5 metres a second. Reducing the athlete's rate 
to a common denominator, we see that he covers seven metres every 
second. These speeds are not absolutely comparable though. Walking, 
you can keep on for hours on end at the rate of 5 km. p.h. But the 
runner will keep up his speed for only a short while. On quick march, 
infantry move at a speed which is but a third of the athlete's, 
doing 2 m/sec, or 7 odd km. p.h. But they can cover a much greater 
distance. 

I daresay you would find it of interest to compare your normal walk- 
ing pace with the "speed" of the proverbially slow snail or tortoise. 
The snail well lives up to its reputation, doing 1.5 mm/sec, or 5.4 metres 
p.h. exactly one thousand times less than your rate. The other clas- 
sically slow animal, the tortoise, is not very much faster, doing usually 
70 metres p.h. 

Nimble compared to the snail and the tortoise, you would find your- 
self greatly outraced when comparing your own motion with other 
motions even not very fast ones that we see all around us. True, 
you will easily outpace the current of most rivers in the plains and be 
a pretty good second to a moderate wind. But you will successfully 
vie with a fly, which does 5 m/sec, only if you don skis. You won't over- 

13 



take a hare or a hunting dog even when riding a fast horse and you can 
rival the eagle only aboard a plane. 

Still the machines man has invented make him second to none for 
speed. Some time ago a passenger hydrofoil ship, capable of 60-70 km. 
p.h., was launched in the U.S.S.R. (Fig. 1). On land you can move faster 




Fig. 1. Fast passenger hydrofoil ship 

than on water by riding trains or motor cars which can do up to 
200 km. p.h. and more (Fig. 2). Modern aircraft greatly exceed even 
these speeds. Many Soviet air routes are serviced by the large TU-104 




fig. 2. New Soviet ZIL-111 motor car 

(Fig. 3) and TU-114 jet liners, which do about 800 km. p.h. It was 
not so long ago that aircraft designers sought to overcome the "sound 
barrier", to attain speeds faster than that of sound, which is 330 m/sec, 



14 



or 1,200 km. p.b. Today this has been achieved. We have some small 
but very fast supersonic jet aircraft that can do as much as 2,000 
km.p.h. 

There are man-made vehicles that can work up still greater speeds. 
The initial launching speed of the first Soviet sputnik was about 




fig. 3. TU-104 jet airliner 

8 km/sec. Later Soviet space rockets exceeded the so-called 
velocity, which is 11.2 km/sec at ground level. 
The following table gives some interesting speed data. 



escape 



A snail 


1.5 mm/ sec or 


5.4 metres p.h. 


A tortoise 


20 or 


70 


A fish 


1 m/scp or 


3.5 km. p.h 


A pedestrian 


1.4 or 


f. r 

D 


Cavalry, pacing 


1.7 or 


6 


M trotting 


3.5 or 


12.fi 


A fly 


5 or 


18 


A skier 


5 or 


18 


Cavalry, galloping 
A hydrofoil ship 


8.5 or 
16 or 


30 
58 


A hare 


18 or 


65 


An eagle 


24 or 


86 


A hunting dog 


25 or 


90 


A train 


28 or 


100 


A ZIL-111 passenger car 


50 or 


170 


A racing car (record) 
A TU-104 jet airliner 


174 or 
220 or 


633 

800 


Sound in air 


330 or 


1,200 


Supersonic jet aircraft 


550 or 


2.000 


The earth's orbital veloc- 






ity 


30,000 " or 


108,000 ' 



15 



RACING AGAINST TIME 

Could one leave Vladivostok by air at 8 a.m. and land in Moscow 
at 8 a.m. on the same day? 

I'm not talking through my hat. We can really do that. The answer 
lies in the 9-hour difference in Vladivostok and Moscow zonal times. 
If our plane covers the distance between the two cities in these 9 hours, 
it will land in Moscow at the very same time at which it took off from 
Vladivostok. Considering that the distance is roughly 9,000 kilome- 
tres, we must fly at a speed of 9,000:9 = 1,000 km. p.h., which is quite 
possible today. 

To "outrace the Sun" (or rather the earth) in Arctic latitudes, 
one can go much more slowly. Above Novaya Zemlya, on the 77th par- 
allel, a plane doing about 450 km. p.h. would cover as much as a definite 
point on the surface of the globe would cover in an identical space of 
time in the process of the earth's axial rotation. If you were flying in 
such a plane you would see the sun suspended in immobility. It would 
never set, provided, of course, that your plane was moving in the 
proper direction. 

It is still easier to "outrace the Moon" in its revolution around the 
earth. It takes the moon 29 times longer to spin round the earth than 
it takes the earth to complete one rotation (we are comparing, naturally, 
the so-called "angular", and not linear, velocities). So any ordinary 
steamer making 15-18 knots could "outrace the Moon" oven in the 
moderate latitudes. 

Mark Twain mentions this in his Innocents Abroad. When sailing 
across the Atlantic, from New York to the Azores "... wo had balmy 
summer weather, and nights that were even finer than the days. We had 
the phenomenon of a full moon located just in the same spot in the 
heavens at the same hour every night. The reason for this singular conduct 
on the part of the mo on did not occur to us at first, but it did afterward 
when we reflected that we were gaming about twenty minutes every day, 
because we were going east so fast we gained just enough every day 
to keep along with the moon. " 



16 



THE THOUSANDTH OF A SECOND 

For us humans, the thousandth of a second is nothing from the angle 
of time. Time intervals of this order have only started to crop up in 
some of our practical work. When people used to reckon the time ac- 
cording to the sun's position in the sky, or to the length of a shadow 
(Fig. 4), they paid no heed to minutes, considering them even unworthy 




Fig. 4. How to reckon the time "according to the 

position of the sun (left), and by the length of a shadow 

(right) 



of measurement. The tenor of life in ancient times was so unhurried 
that the timepieces of the day the sun-dials, sand-glasses and the 
like had no special divisions for minutes (Fig. 5). The minute hand 
first appeared only in the early 18th century, while the second sweep 
came into use a mere 150 years ago. 

But back to our thousandth of a second. What do you think could 
happen in this space of time? Very much, indeed I True, an ordinary 
train would cover only some 3 cm. But sound would already fly 33 cm 
and a plane half a metre. In its orbital movement around the sun, the 
earth would travel 30 metres. Light would cover the great distance of 
300 km. The minute organisms around us wouldn't think the thousandth 



22668 



17 



of a second so negligible an amount of time if they could think of 
course. For insects it is quite a tangible interval. In the space of a 
second a mosquito flaps its wings 500 to 600 times. Consequently in 
the space of a thousandth of a second, it would manage either to raise 
its wings or lower them* 

We can't move our limbs as fast as insects. The fastest thing we can 
do is to blink our eyelids. This takes place so quickly that we fail even 
to notice the transient obscurement of our field of vision. Few know, 
though, that this movement, "in the twinkling of an eye" which has 





Fig. 6. An ancient water clock (loft) and an old pocket- 
watch (right). Note that neither has the minute 
hand 



become synonymous for incredible rapidity is quite slow if measured 
in thousandths of a second. A full "twinkling of an eye" averages as 
exact measurement has disclosed two- fifths of a second, which gives 
us 400 thousandths of a second. This process can be divided into the 
following stages: firstly, the dropping of the eyelid which takes 75-90 
thousandths of a second; secondly, the closed eyelid in a state of rest, 
which takes up 130-170 thousandths; and, thirdly, the raising of the 
eyelid, which takes about 170 thousandths. 

As you see, this one "twinkling of an eye" is quite a considerable time 
interval, during which the eyelid even manages to take a rest. If we 



18 



could photograph mentally impressions lasting the thousandth of a 
second, we would catch in the u twinkling of an eye'* two smooth mo- 
tions of the eyelid, separated by a period during which the eyelid would 
be at rest. 

Generally speaking, the ability to do such a thing would completely 
transform the picture we get of the world around us and we would see 
the odd and curious things that H. G. Wells described in his New Accel- 
erator. This story relates of a man who drank a queer mixture which 
caused him to see rapid motions as a series of separate static phenom- 
ena. Here are a few extracts. 

"'Have you ever seen a curtain before a window fixed in that way 
before?' 

"I followed his eyes, and there was the end of the curtain, frozen, as 
it were, corner high, in the act of flapping briskly in the breeze. 

"'No, 1 said I, 'that's odd.' 

"'And here,' he said, and opened the hand that held the glass. Natu- 
rally I winced, expecting the glass to smash. But so far from smashing 
it did not even seem to stir; it hung in mid-air motionless. 'Roughly 
speaking,' said Gibberne, 'an object in these latitudes falls 16 feet in 
a second. This glass is falling 16 feet in a second now. Only you see, 
it hasn't been falling yet for the hundredth part of a second. [Note also 
that in the first hundredth of the first second of its downward flight a 
body, the glass in this case, covers not the hundredth part of the dis- 
tance, but the 10,000th part (according to the formula S=U2 gt*). This 
is only 0.5 mm and in the first thousandth of the second it would be 
only 0.01 mm.l 

"'That gives you some idea of the pace of my Accelerator.' And he 
waved his hand round and round, over and under the slowly sinking 
glass. 

"Finally he took it by the bottom, pulled it down and placed it 
very carefully on the table. 'Eh?' he said to me, and laughed.... 

"I looked out of the window. An immovable cyclist, head down and 
with a frozen puff of dust behind his driving-wheel, scorched to over- 
take a galloping char-a-banc that did not stir.... 

"We went out by his gate into the road, nnd there we made a minute 
examination of the statuesque passing traffic. The top of the wheels 

2* 19 



and some of the legs of the horses of this char-a-banc, the end of the 
whip lash and the lower jaw of the conductor who was just beginning 
to yawn were perceptibly in motion, but all the rest of the lumbering 
conveyance seemed still. And quite noiseless except for a faint rat- 
tling that came from one man's throat! And as parts of this frozen 
edifice there were a driver, you know, and a conductor, and eleven 
people!... 

"A purple-faced little gentleman was frozen in the midst of a violent 
struggle to refold his newspaper against the wind; there were many evi- 
dences that all these people in their sluggish way were exposed to a 
considerable breeze, a breeze that had no existence so far as our sensa- 
tions went.... 

"All that I had said, and thought, and done since the stuff had begun 
to work in my veins had happened, so far as those people, so far as the 
world in general went, in the twinkling of an eye...." 

Would you like to know the shortest stretch of time that scientists 
can measure today? Whereas at the beginning of this century it was 
only the 10,000th of a second, today the physicist can measure the 
100,000 millionth of a second; this is about as many times less than a 
second as a second is less than 3,000 years! 

THE SLOW-MOTION CAMERA 

When H. G. Wells was writing his story, scarcely could he have 
ever thought he would see anything of the like. However he did live 
to see the pictures he had once imagined, thanks to what has been 
called the slow-motion camera. Instead of 24 shots a second as ordi- 
nary motion-picture cameras do this camera makes many times more. 
When a film shot in this way is projected onto the screen with the 
usual speed- of 24 frames a second, you see things taking place much 
more slowly than normally high jumps, for instance, seem unusually 
smooth. The more complex types of slow-motion cameras will almost 
Simula H. G. Wei Is 's world of fantasy. 



20 



WHEN WE MOVE ROUND THE SUN FASTER 

Paris newspapers once carried an ad offering a cheap and pleasant 
way of travelling for the price of 25 centimes. Several sim- 
pletons mailed this sum. Each received a letter of the following 
content: 

"Sir, rest at peace in bed and remember that the earth turns. At the 
49th parallel that of Paris you travel more than 25,000 km a day. 
Should you want a nice view, draw your curtain aside and admire the 
starry sky." 

The man who sent these letters was found and tried for fraud. The 
story goes that after quietly listening to the verdict and paying the 
fine demanded, the culprit struck a theatrical pose and solemnly de- 
clared, repeating Galileo's famous words: "It turns. 1 ' 

He was right, to some extent, after all, every inhabitant of the 
globe "travels" not only as the earth rotates. He is transported with 
still greater speed as the earth revolves around the sun. Every second this 
planet of ours, with us and everything else on it, moves 30 km in space, 
turning meanwhile on its axis. And thereby hangs a question not devoid 
of interest: When do we move around the sun faster? In the daytime 
or at night? 

A bit of a puzzler, isn't it? After all, it's always day on one side of 
the earth and night on the other. But don't dismiss my question as 
senseless. Note that I'm asking you not when the earth itself moves 
faster, but when we, who live on the earth, move faster in the heavens. 
And that is another pair of shoes. 

In the solar system we make two motions; we revolve around the 
sun and simultaneously turn on the earth's axis. The two motions 
add , but with different results, depending whether we are on the daylit 
side or on the nightbound one. 

Fig. 6 shows you that at midnight the speed of rotation is added to 
that of the earth's translation, while at noon it is, on the contrary, 
subtracted from the latter. Consequently, at midnight we move faster 
in the solar system than at noon. Since any point on the equator travels 
about half a kilometre a second, the difference there between midnight 
and midday speeds comes to as much as a whole kilometre a second. 

21 



Midday 




Midnighi 

Fig. 6. On the dark side we move around the sun faster 
than on the sunlit side 

Any of you who are good at geometry will easily reckon that for 
Leningrad, which is on the 60th parallel, this difference is only half as 
much. At 12 p.m. Leningraders travel in the solar system half a 
kilometre more a second than they would do at 12 a.m. 

THE CART-WHEEL RIDDLE 

Attach a strip of coloured paper to the side of the rim of a cart-wheel 
or bicycle tire, and watch to see what happens when the cart, or bicycle, 
moves. If you are observant enough, you will see that near the ground 
the strip of paper appears rather distinctly, while on top it flashes by 
so rapidly that you can hardly spot it. 

Doesn't it seem that the top of the wheel is moving faster than the 
bottom? And when you look at the upper and lower spokes of the moving 
wheel of a carriage, wouldn't you think the same? Indeed, the upper 
spokes seem to merge into one solid body, whereas the lower spokes 
can be made out quite distinctly. 

22 



Incredibly enough, the top of the rolling-wheel does really move faster 
than the bottom. And, though seemingly unbelievable, the explanation 
is a pretty simple one. Every point on the rolling wheel makes two 
motions simultaneously one about the axle and the other forward 
together with the axle. It's the same as with the earth itself. The two 
motions add, but with different results for the top and bottom of the 
wheel. At the top the wheel's motion of rotation is added to its mo- 
tion of translation, since both are in the same direction. At the bot 
torn rotation is made in the reverse direction and, consequently, must 
be subtracted from translation. That is why the stationary observer 
sees the top of the wheel moving faster than the bottom. 

A simple experiment which can be done at convenience proves this 
point. Drive a stick into the ground next to the wheel of a stationary 
vehicle opposite the axle. Then take a piece of coal or chalk and make two 
marks on the rim of the wheel at the very top and at the very bottom. 
Your marks should be right opposite the stick. Now push the vehicle 
a bit to the right (Fig. 7), so that the axle moves some 20 to 30 cm away 
from the stick. Look to see how the marks have shifted. You will find 
that the upper mark A has shifted much further away than the lower 
one B which is almost where it was before. 





Fig. 7. A comparison between the distances away from 
the stick of points A and B on a rolling wheel (right) shows 
that the wheel's upper segment moves faster than its lower 

part 



THE WHEEL'S SLOWEST PART 

As we have seen, not all parts of a rolling cart-wheel move with the 
same speed. Which part is slowest? That which touches the ground. 
Strictly speaking, at the moment of contact, this part is absolutely 
stationary. This refers only to a rolling wheel. For the one that spins 
round a fixed axis, this is not so. In the case of a flywheel, for instance, 
all its parts move with the same speed. 

BRAIN-TEASER 

Here is another, just as ticklish, problem. Could a train going from 
Leningrad to Moscow have any points which, in relation to the rail- 
road track, would be moving in the opposite direction? It could, we find. 
All the train wheels have such points every moment. They are at the 
bottom of the protruding rim of the wheel (the bead). When the train 
goes forward, these points move backward. The following experiment, 
which you can easily do yourself, will show you how this happens. 
Attach a match to a coin with some plasticine so that the match pro* 
trades in the plane of the radius, as shown in Fig. 8. Set the coin together 
with the match in a vertical position on the edge of a flat ruler and 
hold it with your thumb at its point of contact C. Then roll it to and 
fro. You will see that points F, E and D of the jutting part of the match 





Fig. 8. When the coin is rolled 

leftwards, points F t E and 

D of the jutting part of the 

match move backwards 



Fig. 9. When the train wheel 
rolls leftwards the lower part 
of its rim rolls the other way 





/ig. 10. Top: the curve (a cycloid) described by every 
point on the rim of a rolling cart-wheel. Bottom: the curve 
described by every point on the rim of a train wheel 

move not forwards but backwards. The further point D the end of the 
match is from the edge of the coin, the more noticeable backward 
motion is (point D shifts to D'). 

The points on the bead of the train wheel move similarly. So when 
I tell you now that there are points in a train that move not forward 
but backward, this should no longer surprise you. True, this backward 
motion lasts only the negligible fraction of a second. Still there is, 
despite all our habitual notions, a backward motion in a moving train. 
Figs. 9 and 10 provide the explanation. 

WHERE DID THE YACHT CAST OFF? 

A rowboat is crossing a lake. Arrow a in Fig. 11 is its velocity vector. 
A yacht is cutting across its course; arrow b is its velocity vector. 
Where did the yacht cast off? You would naturally point at once to 
point M. But you would get a different reply from the people in the 
dinghy. Why? 

They don't see the yacht moving at right angles to their own course, 
because they don't realise that they are moving themselves. They think 

25 




Fig. 11. The yacht is cutting across the rowboat's course. Arrows a and b designate 
the velocities. What will the people in the dinghy see? 

they're stationary, while everything around is moving with their own 
speed but in the opposite direction. From their point of view the yacht 
is moving not only in the direction of the arrow b but also in the di- 
rection of the dotted line a opposite to their own direction (Fig. 12). 
The two motions of the yacht the real one and the seeming one are 
resolved according to the rule of the parallelogram. The result is that 
the people in the rowboat think the yacht to be moving along the 
diagonal of the parallelogram 06; that is also why they think the yacht 
cast off not at point M , but at point /V, way in front of the rowboat 
(Fig. 12). 

Travelling together with the earth in its orbital path, we also plot 
the position of the stars wrongly just as the people in the dinghy did 
when asked where the yacht cast off from. We see the stars displaced 
slightly forward in the direction of the earth's orbital motion. Of course, 
the earth's speed is negligible compared with that of light (10,000 




Fig. 12. The people in the dinghy think the yacht to be coming towards them 
slantwise from point N 

times less) and, consequently, this stellar displacement, known as 
aberration of light, is insignificant. However, we can detect it with 
the aid of astronomical instruments. 

Did you like the yacht problem? Then answer another two questions 
related to the same problem. Firstly, give the direction in which the 
yachtsmen think the dinghy is moving. Secondly, say where the yachts* 
men think the dinghy is heading. To answer, you must construct a par- 
allelogram of velocities on the vector a (Fig. 12), whose diagonal will 
indicate that from the yachtsmen's point of view the dinghy seems to 
be moving slantwise, as if heading for the shore. 



CHAPTER TWO 

GRAVITY AND WEIGHT. LEVERS. PRESSURE 



TRY TO STAND UP! 

You'd think I was joking if I told you that you wouldn't be able 
to get up from a chair provided you sat on it in a certain way, even 
though you wouldn't be strapped down to it. Very well, let's have a go. 
Sit down on a chair in the same way the boy in Fig. 13 is sitting. Sit 
upright and don't shove your feet under the chair. Now try to get up 
without moving your feet or bending forward. You can't, however 
hard you try. You'll never stand up until you push your feet under 
the chair or lean forwards. 

Before I explain, let me tell you about the equilibrium of 
bodies in general, and of the human body in particular. A thing will 

not topple only when the perpendicular 
from its centre of gravity goes through 
its base. The leaning cylinder in Fig. 14 
is bound to fall. If, on the other hand, the 
perpendicular from its centre of gravity 
fell through its base, it wouldn't topple 
over. The famous leaning towers of Pisa 
and Bologna, or the leaning campanile in 
Arkhangelsk (Fig. 15), don't fall, despite 
their tilt, for the same reason. The per- 
pendiculars from their centres of gravity 
do not lie outside their bases. Another 

Fig. 13. It's impossible to ieaBon is that their foundations are sunk 
get up deep in the ground. 




You won't fall only when the perpendicular from your centre of 
gravity lies within the area bound by the outer edge of your feet (Fig. 16). 
That is why it is so hard to stand on one leg and still harder to 
balance on a tight-rope. Our "base" is very small and the perpendicular 
from the centre of gravity may easily come to lie outside its limits. 
Have you noticed the odd gait of an "old sea dog"? He spends most of 
his life aboard a pitching ship 
where the perpendicular from 
the centre of gravity of his body 
may come to fall outside his 
"base" any moment. That accus- 
toms him to walk on deck so 
that his feet are set wide apart 
and take in as large a space as 




Fig. 14. The cylinder must 

topple as the perpendicular 

from its centre of gravity 

lies outside its base 




Fig. 15. Arkhangelsk leaning 

campanile. A reproduction from 

an old photograph 



possible, which saves him from falling. Naturally, he'll waddle in the 
same habitual fashion on hard ground as well. 

Another instance of an opposite nature this time. This is when the 
effort to keep one's balance results in a beautiful pose. Porters who 
carry loads on their heads are well-built a point, I presume, you have 
noticed. You may have also seen exquisite statues of women holding 
jars on their heads. It is because they carry a load on their heads that 
these people have to hold their heads and bodies upright. If they 



29 




were to lean in any direction, this would shift the perpendicular 

from the centre of gravity higher than usual, because of the head-load, 

outside the base and unbalance them. 
Back now to the problem I set you at the beginning of the chapter. 

The sitting boy's centre of gravity is inside the body near the spine 
about 20 centimetres above the level of his nave). 
Drop a perpendicular from this point. It will pass 
through the chair behind the feet. You already 
know that for the man to stand up it should go 
through the area taken up by the feet. Conse- 
quently, when we get up we must either bend 
forward, to shift the centre of gravity, or shove our 
feet beneath the chair to place our "base" below 

Fig. 16. When one the centre of gravity. That is what we usually do 

stands the perpendic- wben getting up from a chair. If we are not 

ular from the cen- o r 

tre of gravity passes allowed to do this, we 11 never be able to stand 

boumf^ thcTsoles'of u P~" as you, have already gathered from your own 
one's feet experience. 

WALKING AND RUNNING 

The things you do thousands of times a day, and day after day all 
your life, ought to be things you have a very good idea about, oughtn't 
they? Yes, you will say. But that is far from so. Take walking and 
running, for instance. Gould anything be more familiar? But I won- 
der how many of you have a clear picture of what we really do when we 
walk and run, or of the difference between the two. Let's see what a 
physiologist has to say about walking and running. I'm sure most of 
you will find his description startlmgly novel. (The passage is from 
Prof. Paul Bert, Lectures on Zoology. The illustrations are my own.) 

"Suppose a person is standing on one leg, the right leg, for instance. 
Suppose further that he is lifting his heel, meanwhile bending forwards. 
[When walking or running a person exerts on the ground, when pushing 
his foot away from it, a pressure of some 20kg in addition to 
his weight. Hence a person exerts a greater pressure on the ground 
when he is moving than when standing. V. P.] In such a position the 

30 



perpendicular from the centre of gravity will naturally be outside the 
base and the person is bound to fall forwards. Scarcely has he started 
doing this than he quickly throws forward his left leg, which was 
suspended thus far, to put it down on the ground in front of the per- 
pendicular from the centre of gravity. The perpendicular thus comes 
to drop through the area bound by the lines linking the points of 




Fig. 17. How one walks. The series of positions in walking 

support of both feet. Balance is thus restored; the person has taken 
a step forward. 

"He may remain in this rather tiring position, but should he wish 
to continue forward, he will lean still further forward, shift the per- 
pendicular from the centre of gravity outside the base, and again throw 
his leg the right one this time forwards when about to fall. He thus 



B 



Fig. 18. A graph showing how one's feet move when walking. Line A 
is the left foot and line B is the right foot. The straight sections show 
when the foot is on the ground, and the curveswhen the foot is in the 
air. In the time-interval a both feet are on the ground; in the time- 
interval 6, foot A is in the air and foot B still on the ground; in the 
timeinterval c both feet are again on the ground. The faster ono walks, 
the shorter the time-intervals a and c get (compare with the "run- 
ning" graph in Fig. 20). 



takes another step forward. And so on ana so forth. Consequently, 
walking is just a series of forward fallings, punctually forestalled 
by throwing the leg left behind into a supporting position. 




Fig. 19. How one runs. The series of positions in running, showing 
moments when both feet are in the air 

"Let's try to get to the root of the matter. Suppose the first step 
has already been made. At this particular moment the right foot is 
still on the ground and the left foot is already touching it. If the step 
is not very short the right heel should be lifted, because it is this rising 
heel that enables one to bend forward and change one's balance. It is the 
heel of the left foot that touches the ground first. When next the entire 



\ 



N 

A 



Fig. 20. A graph showing how one's feet move when running 

(compare with Fig. 18). There are time-intervals (6, d and /) 

when both feet are in the air. This is the difference between 

running and walking 

sole stands on the ground, the right foot is lifted completely and no 
longer touches the ground. Meanwhile the left leg, which is slightly 
bent at the knee, is straightened by a contraction of the femoral triceps 
to become for an instant vertical. This enables the half-bent right 



32 



leg to move forward without touching the ground. Following the 
body's movement the heel of the right foot comes to touch the ground in 
time for the next step forwards. The left leg, which at this moment has 
only the toes of the foot touching the ground and which is about to 
rise, goes through a similar series of motions. 

"Running differs from walking in that the foot on the ground is 
energetically straightened by a sudden contraction of its muscles to 
throw the body forwards so that the latter is completely off the ground 
for a very short interval of time. Then the body again falls to come to 
rest on the other leg, which quickly moves forward while the body 
is still in the air. Thus, running consists of a series of hops from one 
foot to the other. " 

As for the energy a person expends in walking along a horizontal 
pavement it is not at all nil as some might think. With every step made, 
the centre of gravity of a walker's body is lifted by a few centimetres. 
A reckoning shows that the work spent in walking along a horizontal 
path is about a fifteenth of that required to raise the walker's body to a 
height equivalent to the distance covered. 

HOW TO JUMP FROM A MOVING CAR 

Most will surely say that one must jump forward, in the direction in 
which the car is going, in conformity with the law of inertia. But what 
does inertia have to do with it all? Til wager that anyone you ask this 
question will soon find himself in a quandary, because according to 
inertia one should jump backwards, contrary to the direction of motion. 
Actually inertia is of secondary importance. If we lose sight of the main 
reason why one should jump forwards one that has nothing to do with 
inertia we will indeed come to think that we must jump backwards 
and not forwards. 

Suppose you have to jump off a moving car. What happens? When 
you jump, your body has, at the moment you let go, the same velocity 
as the car itself by inertia and tends to move forwards. By jumping 
forwards, far from diminishing this velocity, we, on the contrary, in- 
crease it. Then shouldn't we jump backwards since in that case the 
velocity thus imparted would be subtracted from the velocity our body 

32668 33 



possesses by inertia, and hence, on touching the ground, our body would 
have less of a toppling impetus? 

But, when one jumps from a moving carriage, one always jumps 
forwards in the direction of its movement. That is indeed the best way, 
a time-honoured one, and I strongly warn you against trying to test 
the awkwardness of jumping backwards. 

We seem to have a contradiction, don't we? Now whether we jump 
forwards or backwards we risk falling, since our bodies are still moving 
when our feet touch the ground and come to a halt. (See "When Is a 
Horizontal Line Not Horizontal?" from the third chapter of Mechanics 
for Entertainment for another explanation.) When jumping forwards, 
the speed with which our bodies move is even greater than when jump- 
ing backwards, as I have already noted. But it is much safer to jump 
forwards than backwards, because then we mechanically throw a leg 
forwards or even run a few steps, to steady ourselves. Wo do this with- 
Out thinking; it's just like walking. After all, according to mechanics, 
walking, as was noted before, is nothing but a series of forward fallings 
of our body, guarded against by the throwing out of a leg. Since we don't 
have this guarding movement of the leg when falling backwards 
the danger is much greater. Then even if we do fall forwards we can 
soften the impact with our hands, which we can't do if we fall on our 
backs. 

As you see, it is safer to jump forwards, not so much because of inertia, 
but because of ourselves. This rule is plainly inapplicable to one's 
belongings, for instance. A bottle thrown from a moving car forwards 
Stands more chances of crashing when it hits the ground than if thrown 
backwards. So if you have to jump from a moving car and have some 
luggage with you, first chuck out the luggage backwards and then jump 
forwards yourself. Old hands like tramcar conductors and ticket in- 
spectors often jump off stepping backwards but with their backs turned to 
the direction in which they jump. This gives them a double advantage: 
firstly they reduce the velocity that the body acquires by inertia, 
awl, secondly, guard themselves against falling on their backs, as 
they jump with their faces forward, in the direction where they are 
most likely to fall. 



CATCHING A BULLET ' 

The following curious incident was reported during the First World 
War. One French pilot, while flying at an altitude of two kilometres, 
saw what he took to be a fly near his face. Trapping it with his hands, 
he was flabbergasted to find that he had caught a German bullet! How 
like the tall stories told by Baron Munchausen of legendary fame, 
who claimed he had caught cannon balls with bare hands! But there 
is nothing incredible in the bullet-catching story. 

A bullet does not fly everlastingly with its initial velocity of 800- 
900 m/scc. Air resistance causes it to slow down gradually to a mere 
40 m/scc towards the end of its journey. Since aircraft fly with a sim- 
ilar speed, we can easily have a situation when bullet ami plane will 
be flying with the same speed, in which case the bullet, in its relation 
to the piano and its pilot, will be stationary or barely moving. The 
pilot can easily catch it with his hand, especially if gloved, because a 
bullet heats up considerably while whizzing through the air. 



MELON AS BOMB 

We have seen that in certain circumstances a bullet can IOSQ its 
"sting". But there are instances when a gontly thrown "peaceful" 
object has a destructive impact. During the Leningrad-Tiflis motor 
run in 1924, Caucasian peasants tossed melons, apples, and thfe like at 
the racing cars to express their admiration. However, these innocuous 
gifts made terrible dents and seriously injured the motorists. This 
happened because the car's velocity added to that of the tossed melons 
or apples, transforming them into dangerous projectiles. A ten-gramme 
bullet possesses the same energy of motion as a 4kg melon thrown at 
a car doing 120 km.p.h. Of course, the impact of a melon is not the 
same as the bullet's since melons, after all, are squashy. 

When we have super-fast planes doing about 3,000 km.p.h. 
a bullet's approximate velocity their pilots may chance to encounter 
what we have just described. Everything in the way of a super- 
fast aircraft will ram into it. Machine-gun fire or just a chance handful 1 ! 
of bullets dropped from another plane will have the same effect; these: 



bullets will strike the aircraft with the same impact as if fired from a 
machine gun. Since the relative velocities in both cases are the same 
the plane and bullet meet with a speed of about 800 m/sec the de- 
struction done when they collide is the same as well . On the contrary, 
bullets fired from behind at a plane moving with the same speed are 
harmless, as we have already seen. 




Fig. 21. Water-melons tossed at a fast-moving car are as dangerous as bombs 



In 1935 engine driver Borshchov prevented a railway disaster by 
cleverly taking advantage of the fact that objects moving in the same 
direction at practically the same speed come into contact without 
knocking each other to pieces. He was driving a train between Yelnikov 
and Olshanka, in Southern Russia. Another train was puffing along in 
front. The driver of this train couldn't work up enough steam to make 
the grade. He uncoupled his engine and several waggons and set off for 
the nearest station, leaving a string of 36 waggons behind. But as he 
did not place brake-shoes to block their wheels, these waggons started 
to roll back down the grade. They gathered up a speed of some 15 km. 
p.h. and a collision seemed imminent. Luckily enough, Borshchov 
had his wits about him and was able to figure out at once what to do. 
He braked his own train and also started a backward manoeuvre, gradual- 

36 



ly working up the same speed of 15 km.p.h. This enabled him to bring 
the 36 waggons to rest against his own engine, without causing any 
damage. 

Finally this same principle is applied in a device making it easier 
for us to write in a moving train. You all know that this is hard to do 
because of the jolts when the train passes over the rail joints. They do 
not act simultaneously on both paper and pen. So our task is to 




Fig. 22. Contraption for writing in a moving train 

contrive something that would make the jolts act simultaneously on 
both. In this case they would be in a state of rest with respect to each 
other. 

Fig. 22 shows one such device. The right wrist is strapped to the small- 
er board a which slides up and down in the slots in board ft, which, 
in turn, slides to and fro along the grooves of the writing board placed 
on the train compartment table. This arrangement provides plenty of 
"elbow-room" for writing and at the same time causes each jolt to 
act simultaneously on both paper and pen, or rather the hand holding 
the pen. This makes the process as simple as writing on an ordinary 
table at home. The only unpleasant thing about it is that since the 
jolts again do not act simultaneously on both wrist and head, you get 
a jerky picture of what you're writing. 



37 



HOW TO WEIGH YOU RSELF 

You will get your correct weight only if you stand on the scales without 
moving. As soon as you bend down, the scales show less. Why? When 
you bend, the muscles that do this also pull up the lower half of your 
body and thus diminish the pressure it exerts on the scales. On the 
contrary, when you straight en up, your muscles push the upper and 
lower halves of the body away from each other; in this case the scales 
will register a greater weight since the lower half of your body ex- 
erts a greater pressure on the scales. 

You will change your weight-readingsprovided the scales are 
sensitive enough even by lifting an arm. This motion already slightly 
increases your body's seeming weight. The muscles you use to lift your 
arm up have the shoulder as their fulcrum and, consequently, push it 
together with the body down, increasing the pressure exerted on the 
scales. When you stop lifting your arm you start using another, op- 
posite set of muscles; they pull the shoulder up, trying to bring it closer 
to the end of the arm; this reduces the weight of your body, or rather 
its pressure on the scales. On the contrary, when you lower your arm 
you reduce the weight of your body, to increase it when you stop low- 
ering it. In brief, by using your muscles you can increase or reduce 
your weight, meaning of course the pressure your body exerts on the 
scales. 

WHERE ARE THINGS HEAVIER? 

The earth's pull diminishes the higher up we go. If we could lift a 
kilogramme 'weight 6,400 km up, to twice the earth's radius away from 
its centre, the force of gravity would grow 2 2 =4 times weaker, in which 
case a spring balance would register only 250 grammes instead of 1,000. 
According to the law of gravity the earth attracts bodies as if its entire 
mass were concentrated in the centre; the force of this attraction di- 
minishes inversely to the square of the distance away. In our particu- 
lar instance, we lifted the kilogramme weight twice the distance away 
from th? centre of the earth; hence attraction grew 2 2 =4 times 
weaker. If we set the weight at a distance of 12,800 km away from the 
surface of the earth three times the earth's radius the force of attrac- 

38 



tion would grow 3 a =9 times weaker, in which case our kilogramme 
weight would register only 111 grammes on a spring balance. 

You might conclude that the deeper down in the earth \ve were to put 
our one-kilogramme weight, the greater the force of attraction would 
grow and the more it should weigh. However, you would bo mistaken. 
The weight of a body does not increase; on the contrary, it diminishes. 



Downward 
attraction 




Fig. 23. Gravitational pull lessens the closer we get to the 
middle of the Earth 

This is because now the earth's attracting forces no longer act just on 
one side of the body but all around it. Fig. 23 shows you the weight in 
a well; it is pulled down by the fore es below it and simultaneously up 
by the forces above it. It is really only the pull of that spherical part 
of the earth, the radius of which is equal to the distance from the centre 
of the earth to the body, that is of importance. Consequently, the deeper 
down we go, the less a body should weigh. At the centre of the earth 
it should weigh nothing, as here it is attracted by equal forces on all 
sides. 

39 



To sum up: a body weighs most at the earth's surface; its weight 
diminishes whether it is lifted up from the earth's surface or interred 
(this would stand, naturally, only if the earth were homogeneous in 
density throughout). Actually, the closer to its centre, the greater the 
earth's density; at first the force of gravity grows to some distance 
down; only then does it start to diminish. 

HOW MUCH DOES A FALLING BODY WEIGH? 

Have you noticed that odd sensation you experience when you start 
to go down in a lift? You feel abnormally light; if you were falling into 
a bottomless abyss you would feel the same. This sensation is caused 
by weightlessness. At the very first moment when the lift-cabin floor 
has already started to go down but you yourself have still not acquired 
its velocity, your body exerts scarcely any pressure at all on the floor, 
and, consequently, weighs very little. An instant later this queer 
sensation is gone. Now your body seeks to fall faster than the smoothly 
running lift; it exerts a pressure on the cabin floor, reacquiring its 
full weight. 

Tie a weight to the hook of a spring balance and observe the pointer as 
you quickly lower the balance together with the weight. For conveni- 
ence's sake insert a small piece of cork in the slot and observe how it 
moves. The pointer will fail to register the full weight; it will be much 
less! If the balance were falling freely and you would be able to watch 
its pointer meanwhile, you would see it register a zero weight. 

The heaviest object will lose all its weight when falling. The reason 
is simple. ''Weight" is the force with which a body pulls at something 
holding it up or presses down on something supporting it. A jailing 
body cannot pull the balance spring as it is falling together with it. 
A falling body does not pull at anything or press down on anything. 
Hence, to ask how much something weighs when falling is the same as 
to ask how much it weighs when it does not weigh. 

Galileo, the father of mechanics, wrote way back in the 17th century in 
his Mathematical Proofs Concerning Two Fields of a New Science: 
"We feel a load on our back when we try to prevent it from dropping. 
But if we were to drop as fast as the load does, how could it press upon 

40 



and burden us? This would be the same as to try to transfix with a 
spear [without letting go of it Y. P.] somebody running ahead of us 
as fast as we are running ourselves." 

The following simple experiment well illustrates this point. Place 
a nutcracker on one of the scale pans, with one arm on the pan and the 




Fig. 24. Falling bodies are weightless 

other tied by a piece of thread to the hook of the scale arm (Fig. 24). Add 
weights to the other pan to balance the nutcracker. Apply a lighted 
match to the thread. The thread will burn through and the suspended 
nutcracker arm will fall onto the pan. Will tho pan holding the nutcrack- 
er dip? Will it rise? Or will it remain in equilibrium? Since you know 
by now that a falling body weighs nothing, you should be able to give 
the correct answer. The pan will rise for a moment. Indeed, though 
joined to the lower arm the nutcracker's upper arm nevertheless exerts 
less of a pressure on the pan when falling than when stationary. For 
a moment the nutcracker's weight diminishes, and thus the pan hold- 
ing it rises. 

FROM EARTH TO MOON 

The years between 1865 and 1870 saw the publication in France of 
Jules Verne's From the Earth to the Moon, in which he set forth a fan- 
tastic scheme to shoot at the Moon an enormous projectile with people 
inside. His description seemed so credible that most of you who have 

41 



read this book have probably hazarded whether this really could 
be.done. Well, let's discuss it. (Today, after Sputnik and Lunik, we know 
that it is rockets, not cannon projectiles, that will be used for space 
travel. However, since a rocket flies after its last engine burns out, in 
accord with the same laws of ballistics, don't think Perelman is be- 
fi hind the times.) 

Let's see at first whether we can fire a shell 
from a gun at least theoretically so that it nev- 
er f a ii s j 3ac j t ear th again. Theory tells us that 
it's possible. Indeed, why does a shell fired hori- 
zontally eventually fall back on earth again? Be- 
causo the earth attracts it, curving its trajectory. 
Instead of keeping up a straight course, it curves 
towards the ground and is, therefore, bound to 

hit it sooner or later. The earth's surface is also 
curved, but the shell's trajectory is bent still more. 
^ However, if we made the shell follow a trajectory 

curved in exactly the same way as the earth's 
surface it would never fall back on earth again. 
Instead, it would trace an orbit concentric with 
the earth's circumference, becoming its satellite, a 
baby moon. 

But how are we to make the shell follow such 
a trajectory? All we must do is to impart a suf- 
ficient initial velocity. Look at Fig. 25 which 
depicts a cross-section of part of the earth. A can- 
non is mounted on the hilltop at point A. A shell 
fired horizontally from it would reach point B a 
second later if not for the earth's gravitational 
pull. Instead, it reaches point C five metres lower 
than B. Five metres is the distance any freely fall- 
ing body travels (in a void) in the first second 
due to earth's surface gravitational pull. If, after 
Fig. 25. How it drops these* five metres, our shell is at exactly 
to reckon a,projec- t he same distance away from the ground as it was 

vlie S GSC&pB V6- i . i 

lodity when fired at point A, it means that the shell is 



following a trajectory curved concentrically to the earth's circum- 
ference. 

All that remains is to reckon the distance AB (Fig. 25), or, in other 
words, the distance the shell travels horizontally in the space of a 
second, which will tell us the speed we need. In the triangle AOB, the 
side OA is the earth's radius (roughly 6,370,000 m); OC=OA and 
fiC=5m; h nee OB is 6,370,005 m. Applying Pythagoras's theorem we get: 



a (6,370,000) 2 . 

We resolve this equation to find AB equal to roughly 8 km. 

So, if there were no drag a shell shot horizontallyjiwitb a muzzle 
velocity of 8 km/sec would never fall back to earth again] it would be 
an everlasting baby moon. 

Now suppose we imparted to our shell a still greater initial velocity. 
Where would it fly then? Scientists dealing with celestial mechanics 
have proved that velocities of 8, 9 and even 10 km/sec give a trajec- 
tory shaped like an ellipse which would be the more elongated the 
greater the initial .speed is. When the velocity reaches 11.2 km/sec, 
the shell will describe not an ellipse but a non-locked curve, a parabola, 
and fly away from the earth never to return (Fig. 26). So, theoretically it 
is quite possible to fly to the Moon inside a cannon ball, provided its 
muzzle speed is big enough. This, however, is a problem that may 




whenvelociiy is 



Fig. 26. When a projectile is fired with a starting velocity 
of 8 km /sec and more 



present some quite specific difficulties. Let me refer you, for greater 
detail, to Book Two of Physics for Entertainment and also to Inter- 
planetary Travel another book of mine. (In the foregoing we dismissed 
the drag which in real life would exceedingly complicate the attain- 
ment of such great velocities and perhaps render the task absolutely 
impossible.) 

FLYING TO THE MOON: JULES VERNE VS. THE TRUTH 

Any of you who have read From the Earth to the Moon most likely re- 
members the interesting passage describing the projectile's intersection 
of the boundary where the Moon matches the Earth in attraction. Wondrous 
things happened. All the objects inside the projectile became weight- 
less; the travellers themselves began to float in the air. 

There is nothing wrong in all this. What Jules Verne did lose sight 
of was that this happens not only at the point the novelist gave. It 
happens before and after as well in fact, as soon as free flight begins. 

It seems incredible, doesn't it? I'm sure though that soon you will 
be surprised not to have noticed this signal omission before. Let's 
turn to Jules Verne for an example. You haven't forgotten how the 
space travellers ejected the dead dog and how surprised they were to 
see it continue to trail behind the projectile instead of falling back to 
earth. Jules Verne described and explained this correctly. In a void 
all bodies fall with the same speed, with gravity imparting an identical 
acceleration to each. So, owing to gravity, both the projectile and the 
dead dog should have acquired the same falling velocity (an identical 
acceleration). Rather should we say that due to gravity their starting 
velocities diminished in the same measure. Consequently, both should 
whizz along with the same velocity; that is why after its ejection the 
dead dog kept on trailing along in the projectile's wake. 

Jules Verne's omission was: if the dead dog did not fall back to 
earth again after the ejection, why should it fall when inside the pro- 
jectile? The same forces act in both cases! The dead dog suspended in 
mid-air inside the projectile should remain in that state as its speed is 
absolutely the same as the projectile's; hence it is in a state of rest in 
respect to the projectile. 

44 



What goes for the dead dog also goes for the travellers and all objects, 
in general, inside the projectile, as they all fly along the trajectory 
with the same speed as the projectile and should not fall, even though 
having nothing to stand, sit, or lie on. One could take a chair, turn it 
upside down and lift it to the ceiling; it won't fall "down", because 
it will go on travelling together with the ceiling. One could sit on this 
chair also upside down and not fall either. What, after all, could make 
him fall? If he did fall or float down, this would mean that the projec- 
tile's speed would bo greater than that of the man on the chair; other- 
wise the chair wouldn't float or fall. But this is impossible since we 
know that everything inside the projectile has the same acceleration 
as the projectile itself. This was what Jules Verne failed to take into ac- 
count. He thought everything inside the projectile would continue to 
press down on its floor when it was in space. He forgot that a weight 
presses down on what supports it only because this support is stationary. 
But if both object and its support hurtle with the same velocity in 
space they simply can't press down on each other. 

So, as soon as the projectile began to fly further on by its own mo- 
mentum, its travellers became completely weightless and could float 
inside it, just as everything else could, too. That alone would have 
immediately told the travellers whether they wore hurtling through 
space or still inside the cannon. Jules Verne, however, says that in the 
first half hour after the projectile was shot into space they couldn't 
guess whether they were moving or not, however hard they tried. 

"'Nicholl, are we moving?' 

"Nicholl and Barbicane looked at each other; they had not yet trou- 
bled themselves about the projectile. 

"'Well, are we really moving?' repeated Michel Ardan. 

"'Or quietly resting on the soil of Florida?' asked Nicholl. 
"'Or at the bottom of the Gulf of Mexico?' added Michel Ardan. " 

These are doubts a steamboat passenger may entertain; they are 
absolutely out of the question for a space traveller, because he can't 
help noticing his complete loss of weight, which the steamboat pas* 
senger naturally retains. 

Jules Verne's projectile must certainly be a very queer place, a tiny 
world of its own, where things are weightless and float and stay where 

45 



they are, where objects retain their equilibrium wherever they are 
placed, where even water won't pour out of an inclined bottle. A pity 
Jules Verne slipped up, when this offers such a delightful opportunity 
for fantasy to run riot! (If this problem interests you, we could refer 
you to the appropriate chapter in A. Sternfeld's Artificial Earth Sat- 
ellites.) 

FAULTY SCALES CAN GIVE RIGHT WEIGHT 

What is more important to get the right weight scales or weights? 
Don't think both identically important. You can get the right weight 
even on faulty scales as long as you have the right weights. Of the 
several methods used, we shall deal with two. 

One was suggested by the great Russian chemist Dmitry Mendeleyev. 
You begin by placing anything handy on one of the pans. Make sure 
that it is heavier than the object you want to weigh. Balance it with 
weights on the other pan. Then place what you want to weigh on the 
pan holding the weights and remove the necessary number of weights 
to bring to balance again. Tote up the weights removed to get the weight 
of what you wanted to weigh. This is called "the constant load method " 
and is particularly convenient when several objects need to be weighed 
in succession. The initial load is used to weigh everything you have 
to weigh. 

Another method, called the "Borda method" after the scientist who 
proposed it, is as follows: 

Place the object you want to weigh on one of the pans. Then pour 
sand or shot into the other pan till the scales balance. Remove your 
object from' the pan but don't touch the sand or shot in the other 
pan! and place weights in the emptied pan till the scales balance 
again. Tote up these weights to find how much your object weighs. 
This is also called "replacement weighing". 

This simple method can also be used for a one-pan spring balance, 
provided of course you have correct weights. In this case you don't 
need either sand or shot. Just put your object on the pan and note the 
reading. Then remove the object and place in the pan as many weights 
as needed to get the same reading. Their combined weight will give the 
weight of the object they replace. 

46 



STRONGER THAN YOU THINK 



How much can you lift with one arm? Let's say it's ten kilogrammes. 
Does this amount qualify your arm's muscle-power? Oh, no. Your biceps 
is much stronger. Fig. 27 shows how this muscle works. It is attached 
close to the fulcrum of the lever that the bone of your forearm represents. 
The load you are lifting acts on the other end of this live lever. The 
distance between the load and the ful- 
crum, that is, the joint, is almost eight 
times more than that between the end 
of the biceps and the fulcrum. This 
means that if you are lifting a load 
of 10 kg your biceps is exerting eight 
times as much power, and, conse- 
quently, could lift 80 kg. 

It would be no exaggeration to say 
that everybody is much stronger than 
he is, or rather that one's muscles are 
much more powerful than what we 
can really do with them. Is this an 
expedient arrangement? Not at all, 
you might think at first glance. We 
seem to have totally unrewarded loss. 
Recall, however, an old "golden rule" 
of mechanics: whatever you lose in 
power you gain in displacement. Here 
you gain in speed; your arm moves 
eight times faster than its muscles do. 
The muscular arrangement in animals 
enables them to move extremities 
quickly, which is more important 
than strength in the struggle to sur- 
vive. Otherwise, we would move 
around at literally a snail's pace. 




Fig. 27. Forearm C acts as a 
lever. The force acts on point 
7; the fulcrum is at point O 
and the Joad ft is being lifted 
from point B. BO is roughly 
eight times longer thpn 10. 
(This drawing is from an an- 
cient book called Concerning 
the Motions of Animals by the 
17th-century Florentine schol- 
ar Borelli who was the first to 
apply the laws of mechanics 
to physiology.) 



47 



WHY DO SHARP THINGS PRICK? 

Have you ever wondered why a needle so easily pierces things? Why 
is it so easy to drive a needle through a piece of cloth or cardboard and 
so hard to do the same thing with a blunt nail? After all, doesn't the 
same force act in both cases? The force is the same, but the pressure 
isn't. In the case of the needle the entire force is concentrated on its 
point; in the case of the nail the same amount of force is distributed 
over the larger area of the blunt end. So, though we exert the same 
force, the needle gives a much greater pressure than the blunt 
nail. 

You all know that a twenty-toothed harrow loosens the soil more 
deeply than a sixty-toothed one of the same weight. Why? Because the 
load on each tooth of the first harrow is more than on each tooth of the 
second. 

When we speak of pressure, we must always take into consideration, 
besides force, also the area upon which this force acts. When we are 
told that a worker is paid a hundred rubles, we don't know whether 
this is much or little, because we don't know whether this is for a 
whole year or for just one month. 

Similarly does the action of a force depend on whether it is distrib- 
uted over a square centimetre or concentrated on the hundredth of 
a square millimetre. Skis easily take us across fresh snow; without 
them we fall through. Why? On skis the weight of your body is distrib- 
uted over a much greater area. Supposing the surface of our skis is 20 
times more than the surface of our soles, on skis we would exert on 
the snow a* pressure which is only a twentieth of the pressure we exert 
when we have no skis on. As we have noticed, fresh snow will bear you 
when you are on skis, but will treacherously let you down when 
you're without them. 

For the same reason horses used in marshlands are shod in a special 
fashion giving them a wider supporting area and lessening the pressure 
exerted per square centimetre. For the same reason people take the same 
precautions when they want to ci;oss a bog or thin ice, often crawling 
to distribute their weight over a greater area. 

Finally, tanks and caterpillar tractors don't get stuck in loose ground, 

48 



though they are very heavy, again because their weight is distributed 
over a rather great supporting area. An eight-ton tractor exerts a pres- 
sure of only 600 grammes per square centimetre. There are caterpil- 
lars which exert a pressure of only 160 gr/cm 2 despite a two-ton load, 
which makes for the easy crossing of peatbogs and sand-beaches. Here 
it is a large supporting area which gives the advantage, whereas in Ihe 
case of the needle it is the other way round. 

This all shows that a sharpened edge pierces things only because it 
has a very minute area for the force to act upon. That is why a sharp 
knife cuts better than a blunt one: the force is concentrated on a small- 
er area of the knife edge. To sum up: sharp objects prick and cut well, 
because much pressure is concentrated on their points and edges. 

COMFORTABLE BED ... OF ROCK 

Why is it pleasanter to sit on a chair than on a flat-topped stool 
though both arc of wood? Why is it pleasant to lie in a hammock though 
the pieces of rope that go to make it are by no means soft? 

I suppose you've already guessed why. The stool-top is flat; when 
you sit on it, you press down with your entire weight on a small area. 
Chairs, on the other hand, usually have a concave seat; in this case you 
press down on a much greater area, over which your weight is distribut- 
ed. To every unit of surface you have a smaller weight, smaller pres- 
sure. 

The trick, as you see, is to distribute pressure more evenly. On a 
soft bed we make depressions that conform to the uneven shape of our 
bodies. Pressure is distributed rather evenly, with only a few grammes 
per square centimetre. No wonder we find it so pleasant. 

The following reckoning well illustrates the difference. An adult 
person has a body surface of about 2m a , or 20,000 cm 2 . In bed roughly 
a quarter of it 0.5 m a , or 5,000 cm 2 supports him. Presuming that 
he weighs about 60 kg, or 60,000 gr, this would mean that we have a 
pressure of only 12 gr/cm 2 . On bare boards he would have a supporting 
area of only some 100 cm 2 . There are fewer points of contact. This means 
a pressure per sq. cm. of half a kilogramme instead of a dozen grammes. 
Quite a noticeable difference, isn't it? And one feels it at once. 

42668 49 



But even the hardest of beds would be as soft as eiderdown, provided 
the weight of your body were distributed all over it. Suppose you left 
the imprint of your body in wet clay. When it hardens drying clay 
shrinks by some five to ten percent, but we shall discount this you 
could lie in it again and think yourself in a featherbed. Though 
you would be lying on what is practically rock, it would feel soft, 
because your weight would be distributed over a much greater area of 
support. 



CHAPTER THREE 

ATMOSPHERIC RESISTANCE 



BULLET AND AIR 

Every schoolboy knows that the air impedes a bullet in its flight. 
Fow, however, know what a great impediment it is. Most think such 
a "caressing" environment as the air which is something we usually 
never feel could not really get in the way of a fast-flying rifle bullet. 



Fig. 28. Flight of a bullet in the air and in a vacuum. The big arc is the 
trajectory described when there is no atmosphere. The tiny, left-hand arc 

is the real trajectory 

However, one good glance at Fig. 28 will already make you realise 
that the air places quite a serious obstacle in the bullet's way. The 
large curve on the diagram designates the trajectory the bullet would de- 
scribe were there no air. In this case, after flying out of a rifle tilt* 
ed at 45, and with an initial velocity of 620 m/sec, the bullet would 
describe a vast arc ten kilometres high and fly almost 40 km. But actu- 
ally our bullet flies only 4 km, describing the tiny arc which is scarce- 
ly noticeable side by side with the first one. That is what the resist* 
ance of the air, the air drag, does! 

4* 51 



BIG BERTHA 

The Germans were the first in 1918, towards the close of the First 
World War, when French and British aircraft had put a stop to Ger- 
man air raids to practise long-range artillery bombardment from a 
distance of 100 kilometres and more. 




Fig. 29. The range changes when the mouth of a long-distance gun is tilted 

at different angles. In the case of angle 1, the projectile strikes P, and in the 

case of angle 2, P' 9 but in the case of angle 3, it flies much farther as it goes 

through the rarefied stratosphere 



It was by chance that German gunners hit upon their absolutely 
novel method for shelling the French capital, which was then at least 
110 km away from the front lines. Firing shells from a big cannon tilt- 
ed up at a wide angle, they unexpectedly discovered that they could 
make them fly 40 km instead of 20. When a shell is fired steeply up- 
wards with a great initial velocity, it reaches a high-altitude, rarefied 
atmospheric strata, where the air drag is rather weak. Here it flies 
for quite a distance, before veering steeply to fall back to earth again. 
Fig. 29 illustrates the great difference in trajectory at different angles 
of the gun barrel. This became the basic principle of the long-range 
gun that the Germans designed to bombard Paris from 115 km away. 
Such a gun was made Big Bertha and it fired more than 300 shells 
at Paris throughout the summer of 1918. 

52P 



It was learned later that 
Big Bertha consisted of a 
tremendous steel tube 34 me- 
tres long and 1 metre thick. 
The breech walls were 40 cm 
thick. The gun itself weighed 
750 tons. Its 120 kg shells 
were one metre long and 21 cm 
thick. Each charge took 150 kg 
of gunpowder which developed 
a pressure of 5,000 atmos- 
pheres, ejecting the shell with 
an initial velocity of 2,000m/sec. 
Since the angle of elevation 
was 52, the shell described 
a tremendous arc, reaching its 
highest point way up in the 
stratosphere 40 km above the 
ground. It took the shell only 
3.5 minutes to reach Paris, 
115 km away; two minutes were 
spent in the stratosphere. 

Big Bertha was the first 
long-range gun in history, the progenitor of modern long-range artillery. 

Let me note that the greater the initial velocity of a bullet or shell, 
the more resistance the air puts up, increasing, moreover, in proportion 
to the square, cube, etc., of the velocity, depending on its amount. 

WHY DOES A KITE FLY? 

Do you know why a kite soars when pulled forward by the twine? 
If you do, you will also be able to understand why airplanes fly and 
maple seeds float. You'll even be able to fathom to some extent the 
causes of the boomerang's very odd behaviour. Because all these things 
are related. The very same air which is so great an impediment to a 
bullet or a shell enables the light maple seed to float and even heavy 
airliners to fly. 




Fig. 30. Big Bertha 



53 



M 





If you don't know why a kite flies, 
the simple drawing in Fig. 31 will pro- 
vide the explanation. Let line MN des- 
ignate the kite's cross-section. When 
you let the kite go and pull at the cord, 
the kite, because of its heavy tail, moves 
at an angle to the ground. Let the kite 
move from right to left and a be the 
angle at which the plane of the kite is 
inclined to the horizon. We shall now 
proceed to examine the forces that act 
on the kite. The air, of course, should 
obstruct its movement and exert some 
pressure on it, designated on Fig. 31 by 
the vector OC. Since the air always presses 
perpendicular to the plane, OC is at 

right angles to MN. The force OC may be resolved into two forces by 
constructing what is called a parallelogram of forces. This gives us the two 
forces OD and OP. Of these two, the force OD pushes the kite back, 
thus reducing its initial velocity. The other force, OP, pulls the kite up, 
reducing its weight. When this force is big enough it overcomes the 
weight of the kite and lifts it. That is why the kite goes up when 
you pull it forwards. 

The airplane is also a kite really, with the difference that its forward 
motion, which makes it go up, is imparted not by our pulling at it 
but by the propeller or jet engine. This is, of course, a very crude ex- 
planation. There are other factors that cause an airplane to rise. They 
are explained in Book Two of Physics for Entertainment under the 
heading "Waves and Whirlwinds". 



Fig. 31. The forces that 
make a kite fly 



LIVE GLIDERS 



As you see aircraft are not made like birds, as one usually thinks, 
but rather like flying squirrels or. flying fish, which, by the way, em- 
ploy their flying mechanism not to fly up but merely to take rather big 
leapsor what a flier would call "glides". In their case, the force OP 



54 



(Fig. 31) is too small to offset 
their weight; it merely reduces 
their weight, enabling them to 
make very big jumps from some 
high point (Fi. 32). A flying 
squirrel can jump 20-30 m from 
the top of one tree to the lower 
branches of another. In the East 
Indies and in Ceylon a much 
larger species of flying squirrel is 
found. This is the kaguan, a fly- 
ing lemur, which is about the size 
of our house cat and which has a 
wing spread of about half a me- 
tre, enabling it to leap some 50 m, 
despite its great weight. As for 
the phalangers that inhabit the 
Sunda Isles and the Philippines, 
they can jump as far as 70 m. 




Fig. 32. Flying squirrels jump from 
20 to 30 m 



BALLOONING SEEDS 

Plants also often employ a gliding mechanism to propagate. 
Many seeds have either a parachuting tuft or hairy appendages (the 
pappus), as in dandelions, cotton balls, and "goat's beards", or "wings", 
as in conifers, maples, white birches, elms, lindens, many kinds of 
umbel liferae, etc. 

In Kerner von Marilaum's well-known Plant Life, we find the follow- 
ing relevant passage: 

"On windless sunny days a host of seeds and fruits are lifted high 
up by vertical air currents. However, after dusk they usually float 
down a short cry away. It is important for seeds to fly, not so much 
to cover a wide area as to inhabit cracks in terraces and cliffs, which 
they would never reach in any other way. Meanwhile, horizontal air 
currents may carry these hovering seeds and fruits rather far. 

"The seeds of some plants retain their wings and parachutes only 
while they fly. Thistle seeds quietly float until they encounter an 



55 




obstacle, when the seed discards its para- 
chute and drops to the ground. That is 
why we see the thistle so often near 
walls and fences. But there are other 
cases, when the seed is attached per- 
manently to its parachute." 




Fig. 33. Fruit of "goat's 
beard M 



Fig. 34. Winged seeds of a) maple, 6) pine-tree, 
c) elm, and d) birch 



Figs. S3 and 34 show some seeds and fruits that have a gliding 
mechanism. As a matter of fact these pJant "gliders" beat man-made 
ones on many points. They can lift a load which may be much greater 
than their own weight and automatically stabilise it. Thus if the 
seed of the Indian jasmine should chance to turn over, it will autom- 
atically regain its initial position with its convex side bottom-most, 
but when it meets an obstacle it doesn't capsize and drop like a plum- 
met, but coasts down instead. 



DELAYED PARACHUTE JUMPING 

This, naturally, brings to mind the brave jumps parachutists some- 
times make. They bail out at altitudes of some ten kilometres and pull 
the ripcord only after plummeting like a stone without opening their 
parachutes for quite a distance. Many think that in this delayed jump 



56 



the parachutist falls as if in empty space. If this were really so, the 
delayed jump would be a much shorter affair, while the near-ground 
velocity would be tremendous. 

However, atmospheric resistance prevents acceleration. The velocity 
of the falling parachutist during a delayed jump increases only in the 
first ten seconds, only for the first few hundred metres. Meanwhile 
atmospheric resistance increases, to finally reach a point where all 
further acceleration stops and the falling becomes even. 

Here is a crude idea of a delayed jump from the angle of mechanics. 
Acceleration continues for only the first 12 seconds or even less, de- 
pending on the parachutist's weight. In this period he drops some 400- 
450 m and works up a velocity of about 50 m/sec. After that he falls 
uniformly, with the same speed, until he pulls the ripcord. Raindrops 
fall similarly. The only difference is that the initial period of accel- 
eration for the raindrop is no more than a second. Consequently its 
near-ground velocity is not so great as in a delayed parachute jump, 
being between 2 and 7 metres a second, depending on its size. (Read 
my Mechanics for Entertainment for more about raindrop velocity and 
my Do You Know Your Physics? for more about delayed parachute 
jumping.) 

THE BOOMERANG 

For long this ingenious weapon, the most perfect technical device 
primitive man ever invented, had scientists wondcrstruck. Indeed, 
the queer tangled trajectory the boomerang traces (Fig. 35} can 
tease any mind. Nowadays we have an elaborate theory to explain 
the boomerang; it is no longer a wonder. This theory is too intricate 
to explain at length. Let me merely note that boomeranging is the 
combined result of three factors: firstly, the initial throw; secondly, 
the boomerang's own rotation, and thirdly, atmospheric resistance. 
The Australian aborigine instinctively knows how to combine all 
three, deftly changing the boomerang's tilt and direction, and he 
throws it with a greater or smaller force to obtain the desired result. 

You, too, can acquire some knack in boomerang-throwing. To 
make one for indoors, cut it out of cardboard, in the form shown in 
Fig. 36. Each arm is about 5 cm long and a little less than a centimetre 

57 




*ig. 35. r Australian aborigine throwing a boomerang. The dotted line shows 
the trajectory of the boomerang, should it miss its target 





Fig.36. A cardboard boomer- 
ang and how to "throw" it 



Fig. 37. Another cardboard 
boomerang (real size) 



58 



wide. Press it under the nail of your thumb 
and flick it forwards and a bit upwards. 
It will fly some five metres, loop, and 
return to your feet, provided it doesn't 
hit anything on the way. You can make 
a still better boomerang by copying the 
one given in Fig. 57, and also by twisting 
it to look somewhat like a propeller (as 
shown at the bottom of Fig. 37). After 
some experience you should be able to 
make it describe intricate curves and loops 
before it returns to your feet. 

In conclusion let me note that the boomer- 
ang is not at all exclusively an Australian 
missile as is usually thought. It was em- 
ployed in India and according to extant mu- 
rals it was once commonly used by Assyrian 

warriors (see Fig. 38). It was also familiar in ancient Egypt and Nubia. 
The Australian boomerang's only distinguishing feature is the propel- 
ler-like twist that we mentioned, send ing it into such a maze of whirls 
and loops, returning it to the thrower, should he miss. 




Fig. 38. Ancient Egyptian 
warrior throwing a boomer- 
ang 



CHAPTER FOUR 

ROTATION. "PERPETUAL MOTION" MACHINES 



HOW TO TELL A BOILED AND RAW EGG APART? 

How can we find out whether an egg is boiled Jor not, without break- 
ing the shell? 

Mechanics gives us the answer. The whole trick is that a boiled egg 
spins differently than a raw one. Take the egg, place it on a flat plate 
and twirl it (Fig. 39). A cooked egg, especially a hard-boiled one, will 
revolve much faster and longer than a raw one; as a matter of fact, 
it is hard even to make the raw egg turn. A hard-boiled egg spins so 
, quickly that it takes on the hazy form of a flat white ellipsoid. 
If flicked sharply enough, it may even rise up to stand on its narrow 
end. 

The explanation lies in the fact that while a hard-boiled egg re- 
volves as one whole, a raw egg doesn't; the latter's liquid contents do not 





Fig. 39. Spinning an egg 



Fig. 40. Telling a boiled 
from a raw one. 



60 



have the motion of rotation imparted at once and so act as a brake, 
retarding by force of inertia the spinning of the solid shell. Then boiled 
and raw eggs stop spinning differently. When you touch a twirling 
boiled egg with a finger, it stops at once. But a raw egg will resume spin- 
ning for a while after you take your finger away. Again the force of 
inertia is responsible. The liquid contents of the raw egg still continue 
moving after the solid shell is brought to a state of rest. Meanwhile 
the contents of the boiled egg stop spinning together with the outer 
shell. 

Here is another test, similar in character. Snap rubber bands around 
a raw egg and a boiled one, along their "meridian", as it were, 
and hang them up by two identical pieces of string (Fig. 40). Twist the 
strings, giving the same number of turns, and then let them go. You will 
spot the difference between the two eggs at once. Inertia causes the boiled 
egg to overshoot its starting position and give the string some more 
twists in the opposite direction; then the string unwinds again with the 
egg again giving several turns; this continues for some time, the number 
of twists gradually diminishing until the egg comes to rest. The raw egg, 
on the other hand, scarcely overshoots its initial position at all; it will 
give but one or two turns and stop long before the boiled egg does. As 
we already know, this is due to its liquid contents which impede its 
movement. 

WHIRLIGIG 

Open an umbrella, stand it up with its top on the floor and twist the 
handle. You can easily make it revolve rather quickly. Now throw a 
little ball or a crumpled piece of paper into the umbrella. It won't stay 
there; it will be shot out by what has wrongly come to be called the 
"centrifugal force" but which is actually nothing but a manifestation 
of the force of inertia. The ball or piece of paper will be thrown off, not 
along the continuation of the radius but at a tangent to the circular mo- 
tion. 

At some public parks one may find an amusement (Fig. 41) based on 
this principle of rotation, where you may try out the law of inertia on 
yourself. This is a sort of whirligig with a round floor on which people 
either stand, sit, or lie. A concealed motor starts the floor revolving, 

61 




Fig. 41. A whirligig. Centrifugal forces are hurling the boys off 

increasing its speed till inertia makes everybody on it slither or slide 
towards its edge. At first this is hardly noticeable, but the further away 
one gets from the centre, the more noticeable do both speed and, conse- 
quently, inertia grow. You try hard to hold on, but it is to no avail and 
finally you are hurled off. 

The Earth itself is, in point of fact, a huge whirligig. Though it doesn't 
burl us off, it does reduce our weight. At the equator, where rotation 
is fastest, one can "shed" a 300th of one's weight in this manner. 
This, plus another factor, the Earth's compression, reduces weight at 
the equator by about 0.5% or 1 /200th. An adult person will con- 
sequently weigh 300 grammes less at the equator than at any of 
the poles. 

INKY WHIRLWINDS 

Make a teetotum, as shown in life size in Fig. 42, out of white card- 
board and a match sharpened at one end. No particular knack is needed 
to twirl it it's something any child can do. But though a child's 
toy, it can be very instructive. Do the following. Spill a few drops 
of ink on it and set it spinning before the ink dries. When it stops, look 

62 




Fig. 42. Ink drop traces on a twirling teetotum 

to see what has happened to the ink drops. They will have drawn 
whorls a miniature whirlwind. 

Incidentally, this resemblance is not accidental. The whorls on the 
teetotum trace the movement of the ink drops, which undergo exactly 
what you experienced on the revolving floor. As the drop shoots away 
from the centre due to centrifugal forces, it reaches a place on the 
teetotum having a greater speed of rotation than the speed of the drop 
itself. Here the disc spins faster than the drop which seems to glide away, 
lagging behind the radial "spokes", as it were. That is why the drops 
curve, and we see the trace of curvilinear motion. 

The same is true for air currents diverging from a centre of high at- 
mospheric pressure (in "anticyclones"), or converging in a centre of 
low atmospheric pressure (in "cyclones"). The ink whorls depict these 
stupendous whirlwinds in miniature. 

THE DELUDED PLANT 

The centrifugal force produced by fast rotation may even outvie 
gravity, a point that was demonstrated by the British botanist Knight 
more than a hundred years ago. It is common knowledge that a young 
plant always directs its stem contrary to gravity, or, in plain language, 

63 




Fig. 43. Seeds germinating on the rim 
of a spinning wheel stem towards the 
axle and send their roots outwards 



grows upwards. Knight, however, 
caused seeds to sprout inwards, 
from the outer rim of a quickly- 
spun wheel. The roots, on the 
other hand, were directed outwards 
(Fig. 43). He was able to fool the 
plant, as it were, substituting cen- 
trifugal force for gravity. The ar- 
tificial gravity proved to be more 
powerful than the earth's natural 
pull by the by, the modern theory 
of gravity does not present any 
objections, in principle, to this 
explanation. 



"PERPETUAL MOTION" MACHINES 

"Perpetual motion" is a topic that comes in for frequent mention, 
but I don't think all realise what it actually means. The "perpetual 
motion" machine is an imagined mechanism which continues its motion 
without end and meanwhile can also do some useful work, as lifting a 
load, for instance. It has never been constructed, though attempts 
have been made since ancient times. The futility of this task gave 
rise to the firm conviction that a "perpetual motion" machine is im- 
possible, and to the law of the conservation of energy fundamental 
for modern science. "Perpetual motion" as such is endless motion with- 
out any work done. 

Fig. 44 depicts one of the oldest projects of a "perpetual motion" 
machine which certain cranks try to revive even now. Attached to the 
rim of the wheel are rods with weights at their ends. In any position 
of the \\hcel the weights on the right-hand side are farther from the 
centre than those on the left-hand side. Consequently, the right-hand 
weights should always outweigh the left side, thus compelling the wheel 
to turn. Hence the wheel should spin for ever, or at least until its axis 
wears through. That at any rate was what its inventor thought. Don't 
try to make such a machine. It will never turn. Why? 



64 



Though the right-hand weights are always farther from the centre, 
you are sure to have a position when they will be less in number than 
those on the left-hand side. Look at Fig. 44 once again. You see only 
four right-hand weights and eight left-hand ones. The entire arrange- 
ment is thus balanced. The wheel will never turn; it will only swing 
a bit and then come to rest in this position. (The motion of this ma- 
chine is explained by the so-called theorem of momenta.) 

It has been proved beyond doubt that a "perpetual motion" machine 
as a source of energy is absolutely impossible. It is futile to undertake 
this task, which alchemists of yore, especially of the Middle Ages, racked 
their brains in vain to solve, thinking it even more tempting than 
the "philosopher's stone". The famous 19th-century Russian poet Push- 
kin describes such a dreamer, one Berthold, in his Chivalrous Episodes. 

"'What is perpeluum mobile?' Martin inquired. 

"'Perpetuum mobile,' Berthold returned, 'is perpetual motion. If 1 
find perpetual motion I sec no bounds to man's creative endeavour. 
For, my good Martin, while the making of gold is entrancing, a dis- 
covery perhaps, both curious and profitable, the finding of per^etuum 
mobile.... Ah, how grand that would be! 1 " 

Hundreds of "perpetual motion" machines were invented, but none 
ever moved. Every inventor invariably omitted something that "upset 
the apple-cart". 





Fig. 44. An "everlastingly" 

moving wheel of the Middle 

Ages 



Fig. 45. A "perpetual motion" 

machine with balls rolling in 

compartments 




Fig. 46. Fake pcrpcluum mobile as an advertisement 
for a Los Aiigcles cafe 

Fig. 45 depicts^another "supposed "perpetualf motion" machine a 
wheel with heavy balls rolling in" compartments between the outer 
rim and huh. The idea. was that the balls closer to the outer rim on 
one side of the wheel would compel the wheeHo turn by their weight. 

But this will never happenfor the same reason as the wheel in Fig. 
44 doesn't turn. Still, in Los Angeles a tremendous wheel of this nature 
(Fig. 46) was built to advertise a cafe. Actually it was a fake, being 

66 



turned by an artfully concealed mechanism though people thought 
it was spun by the heavy balls rolling in the compartments. Other 
such fake "perpetual motion" machines, all set in motion by electricity, 
were placed in the windows of watchmaker's shops to attract the eye 
of the public. 

Incidentally, one ad of this nature [impressed my students so 
greatly that they wouldn't believe me when I told them that perpetual 
motion was impossible. Seeing is believing, they say, and when my 
students saw the balls rolling and turning the wheel, it seemed far 
more convincing than anything 1 could say. I told them that the fake 
"wonder" machine was driven by electricity from the city mains but 
that didn't help cither. Then I recalled that on Sundays tho electricity 
was cut off.. So I advised my pupils to call on the shop on a Sunday. 

"Did you see the 'perpetual motion' machine in action? w I asked 
afterwards. 

"No," they replied, their heads aLanging, "it was covered up with a 
newspaper. " 

The law of the conservation of energy regained their confidence and 
they never lost faith in it again. 

"THE SNAG" 

Many ingenious home-taught Russian inventors tackled the fasci- 
nating problem of a "perpetual motion" machine. One, the Siberian 
peasant Alexander Shcheglov, is described under the name of Burgher 
Prezentov by the well-known 19th-century Russian satirist Saltykov- 
Shchedrin in his Modern Idyll. Below the writer describes a visit to the- 
inventor's workshop: 

"Burgher Prezentov was a man of some 35 summers, gaunt and pale 
of face. He had large pensive eyes and long hair which fell in strands 
onto his neck. Half of his rather roomy cottage^ was taken up by 
a big flywheel and \\e barely managed to squeeze in. It was a spoked 
wheel and had a rather large outer rim of boards nailed together like 
a box. Inside it was empty, and held tho mechanism, the inventor's 
secret. There was nothing particularly cunning about it merely bag* 
of sand which were to balance one another. A stick in the spokes kept 
the wheel stationary. 

5* 67 



' "'We've heard that you've applied the law of perpetual motion in 
practice. Is that true?' I began. 

"'I really don't know how to put it/ he returned in confusion. '1 
think I've done it.' 

"'Can we take a look?' 

"Tray, do! I'll be delighted.' 

"He led us up to the wheel and then took us around to the other side.. 
It was a wheel all right, from either side. 

"'Does it turn?' 

"'Well, it should. But it's a bit capricious.' 

"'Can you take the stick out?' 

"Prezentov removed it, but the wheel stood still. 

"'It's up to its tricks again! 1 he repeated. 'It needs an impetus.' 

"He gripped the rim with bolh hands, swung it back and forth sever* 
al times, then pushed it with all his might. Th? wheel began to turn. 
It made several turns rather quickly and smoothly. One could hear 
the bags of sand inside the rim banging against the boards and sliding 
away. Then the wheel began to turn more and more slowly. We heard 
a rasping and a creaking and, finally, the wheel stopped altogether. 

"'Must be a snag somewhere,' the inventor explained in confusion 
as he strained and swung the wheel again. But the result was the same. 

"'Perhaps you forgot friction?' 

U 'I didn't.... Friction you ay? It's not because of that. Friction's 
nothing. Sometimes it make? you happy and then, bang, it's up to 
its tricks, gets ornery, and that's that. If the wheel were made of real 
stuff, not scraps!'" 

It was of course not the "snag" or the "real stuff" that was at fault, but 
. the wrong principle at the root. The wheel turned for a time owing to 
the impetus that the inventor gave it, but was bound to stop when 
friction exhausted the imparted outside energy. 

"IT'S THEM BALLS THAT DO IT" 

, The writer Karonin (the pen-name of N. Y. Petropavlovsky) describes 
.another Russian "perpetual motion" machine inventor in his story 
"Perpetuum Mobile". This was Lavrenti Goldyrev, a peasant from 

,68 



Perm Gubernia who died in 1884. Karon in, who changed the name in' 
the story to Pykhtin, describes the machine in great detail. 

"Before us was a large queer machine resembling at first glance 
the sort of thing a blacksmith uses to shoe horses on. We could see some 
badly planed wooden pillars and beams and a whole system of flywheels 
and gear wheels. It was all a very clumsy-looking affair, rough and' 
ugly. Several iron balls lay on the floor underneath the machine and 
there was a whole pile of them a bit to the side. 

"'Is that it?' the major-domo asked. 

44 'That's it.' 

"'Well, does it turn?' 

44 'How else?' 

"'Have you got a horse to turn it?' 

"'A horse? What for? It turns by itself,' Pykhtin returned and began 
to demonstrate the monster's workings. 

"The main role was played by iron balls heaped up nearby. 

"'It's them balls that do it. Look. First it goes whack into this 
scoop. Then it flies like lightning along that groove, is scooped 
up by that scoop, flies like mad back Co that wheel and again gives 
it a good push so hard thai it even begins to whine. Meanwhile another 
ball is on its way. Again it flies along and goes whack here. From here 
it dashes plong the groove and strikes that scoop, skips to the wheel, 
and again uhack! That's how it goes. Wait, I'll start it off.' 

"Pykhtin darted to and fro, hastily collecting the scattered balls. 
Finally, after heaping them up into a pile by his feet, he picked one 
up and threw it with all his mi^l.t at the nearest scoop on the wheel. 
Then he quickly picked up a second, then a third. The noise was some- 
thing unimaginable. The balls clanked against the iron scoops, the 
wheel creaked, the pillars groaned. An infernal whine and racket filled 
this gloomy place." 

Karonin claims that Goldyrev's machine moved. But this was pat- 
ently a misunderstanding. The wheel could have turned only \ihile 
the balls were dropping down at the expense of the potential energy 
accumulated when lifted, much in the manner of the weights of a pen- 
dulum clock. However, it couldn't have turned long because when all 
the lifted balls had "whacked" against the scoops and had slipped 

69. 



down, it would stop provided it hadn Vstopped before by the counter- 
effect of all the balls it was supposed to lift. 

Later on, Goldyrev became disappointed in his invention when at 
an exhibition in Yekaterinburg, where he showed it, he saw real in- 
dustrial machines. When asked about his "perpetual motion" contrap- 
tion, he dejectedly replied: "The L devil take it! Tell 'em to chop it up 
for firewood." 

UFIMTSEV'S ACCUMULATOR 

Ufimtsev's so-called accumulator of kinetic energy well illustrated 
the pitfalls that may trap a cursory observer of a "perpetual motion" 
machine. Ufimtsev, an inventor from Kursk, devised a new kind of 
windmill power station with a cheap flywheel type of "inertia accumu- 
lator". In 1920 ho built a model of it, shaped as a disc that spun round 
a vertical axis set on ball bearings inside an air-free jacket. When revved 
to 20,000 r.p.m., the disc was able to turn for 15 days on end. The 
unthinking observer could well believe that ho had before him a real 
"perpetual motion" machine* 



"A MIRACLE, YET NOT A MIRACLE" 

The futile search for a "perpetual motion" machine clouded many 
lives. I once knew a factory worker who sank into absolute destitution, 
spending all his earnings and savings in the delusion that he could 
make a "perpetual motion" machine. Poorly clad and always hungry, 
he^would beg everyone he met to give him some money to make the 
"finished model", which would "certainly move". It was a great pity 
to sec this man suffering so much only because of his ignorance of the 
rudiments of physics. 

It is curious to note that whereas the search for a "perpetual motion" 
machine was always abortive, the profound realisation of its impossi- 
bility, on the contrary, often led to discoveries of great value. 

A wonderful illustration in point is the method which the remark- 
able Dutch scientist Stevin, who lived at the turn of the 16th cen- 
tury, evolved to establish the law of the equilibrium of forces on an 

TO 




inclined plane. He deserves far greater fame than befell him for his 
many major discoveries that we now constantly address ourselves to. 
These are decimal fractions, the introduction of denominators in al- 
gebra, and the establishment of the hydrostatic law that Pascal redis- 
covered later. 

Stevin evolved the law of the equilibrium of forces on an inclined 
plane without invoking the rule of the parallelogram of forces. He 
proved it with the aid of a drawing, 
which is reproduced in Fig. 47. A 
chain of fourteen identical spheroids 
is slipped round a three-sided prism. 
What happens to it? The bottom, 
which droops garland-like, is in a 
state of balance, as you see. But do 
the other two [parts balance each 
other? In other words, do the two 
spheroids on the right offset the four 
on the left? The answer is yes. Other- 
wise the chain would keep on rolling 
of its own accord from right to left 
for ever. Otherwise other spheroids 

take the place of those that slide "'off and "equilibrium would 
never be restored. But we know that a chain disposed in Ibis fashion 
does not move of its own accord at all It is quite obvious that the two 
spheroids on the right really offset the four on the loft. 

It seems a minor miracle, doesn't it? Two spheroids pull with the 
same force as four! This enabled Stevin to deduce an important law 
of mechanics. This is how he reasoned. The two parts the long one 
and the short one possess a different weight, ono being as many times 
heavier than the other as the longer side of the prism is longer than the 
short side. Consequently, any two linked lofds in general balance on 
tilted planes, provided their weight is directly proportional to the 
length of these planes. 

When the short plane is vertical we get a well-known law of mechan- 
ics, which is: to hold a body in place on a tilted plane we must act 
in the direction of this plane with a force as many times loss the weight 



Fig. 47. "A miracle, yet 
not a miracle" 



of -the body as the length of the plane is greater than its height. So* 
did the idea that a "perpetual motion" machine is impossible led to 
an important discovery in the realm of mechanics. 

MORE "PERPETUAL MOTION" MACHINES 

Fig. 48 shows a heavy chain fitted around wheels in such a way 
that the right-hand part is always longer than the left-hand part, 
whatever its position. The inventor thought that since the right-hand 

part would always weigh more than the left- 
hand part, it would always outweigh the 
left-hand part and thus cause the entire ar- 
rangement to keep going. But does this really 
happen? Of course not. You already know 
that the [heavier part of a chain may be 
offset by the lighter part, provided they are 
pulled by forces acting at different angles. In 
this particular system, the left-hand part of 
the chain 'droops vertically down, while the 
right-hand part is inclined. So, though it is 
heavier, still it cannot pull over the left-hand 
part and we do not achieve the "perpetual 
motion" expected. 

I think the cleverest "perpetual motion" 
machine ever invented was one displayed at 
the Paris Exposition in the 1860's. It consisted 
of a large wheel with balls rolling about in 
its compartments. The inventor claimed that 
nobody would ever be able to stop the wheel. 




r 



fig. 48. Is this a "perpot- Many visitors tried to stop it but it went on 
ual motion" machine? turning as soon as they took their hands off 

it. Not a single person realised that the wheel 

turned precisely because of the effort he made to stop it. The backward 
push he gave to stop it wound up the spring of an artfully concealed 
mechanism. 



72 



THE "PERPETUAL MOTION" MACHINE PETER 
THE GREAT WANTED TO BUY 

Preserved in archives is a bulky correspondence which Peter the 
Great of Russia carried on between 1715 and 1722, when he wanted 
to buy a "perpetual motion" machine that had been devised in 
Germany by one Councillor Orffyreus. This man whose "self-moving 
wheel" won him nation-wide fame consented to sell it to the tsar 
only fora princely sum. Peter the Great's librarian Schumacher, whom 
the tsar had sent to Western Europe to collect rare oddities, reported 
the following, when asked to negotiate the purchase: 

"The inventor's last words were: One hundred thousand thalers and 
you get the machine. " 

As for the machine itself, according to Schumacher, the inventor 
claimed that it was no fake and that it could not be defamed "except 
out of malice, and the whole world is full of spiteful people whom 
one cannot believe". 

In January 1725 Peter the Great decided to go to Germany to see 
this notorious "perpetual motion" machine himself, but he died 
before he could accomplish his purpose. 

Who was this mysterious Councillor Orffyreus and what was his 
"famous machine" really like? I was able to learn something both 
about the Councillor himself and his machine. 

Orffyreus 's real name was Bessler. He was born in Germany in 1680. 
He studied theology, medicine and painting before he essayed the "per- 
petual motion" machine. Among the many thousands who tried to 
invent such a machine he is probably the most famous and, at any rate, 
the luckiest. Till the end of his days he died in 1745 he lived in 
comfort on the income he netted by demonstrating his contraption. 

Fig. 49 is a reproduction of a drawing from an old book depicting 
Orffyreus's machine as seen in 1714. It shows a large wheel which ap- 
parently not only turned by itself, but even lifted a heavy load to quite 
a height. 

The fame of this "miracle" machine, which the learned councillor 
first exhibited at various market fairs, quickly spread throughout 
Germany. Soon Orffyreus acquired powerful patrons. The Polish 

73 




Fig. 49. Orffyreus's self-moving wheel which Peter the Great wanted to buy. (From 

an old drawing.) 

king displayed interest and then the Landgrave of Hesse-Cassel patron- 
ised the inventor, placing his castle at the latter's disposal and sub- 
jecting the machine to every kind of trial. 

On November 12, 1717, the machine was placed in a room all apart 
and set into motion. The room was then locked and sealed, and two 
grenad iers" were posted outside. For a whole fortnight, until the seal 
was broken on November 26, no one dared to come near. Thon the room 
was unlocked and the Landgrave and his retinue entered. The wheel 
was still spinning "with undiminishing speed". It was stopped, in- 
spected carefully, and again set going. Now the room was locked and 
sealed for 40 days on end with grenadiers again stationed at the 
door. The seal was broken on January 4, 1718. A commission of experts 
entered and found that the wheel was still going. But this did not sat- 
isfy the Landgrave and he staged a third trial, locking up the machine 
for two whole months at a stretch. When he found the wheel still going 

74 



oven after that, he was delighted. He granted the inventor a parchment 
to certify that his "perpetual motion" machine did 50 revolutions 
per minute, could lift 16 kg to the height of 1.5 m and could also work 
a grinder and bellows. With this document in his pouch, Orffyreus 
travelled the length and breadth of Europe. He apparently netted a 
princely income, considering that he consented to sell his machine 
to Peter the Great for not less than 100,000 rubles. 

The fame of the councillor's marvel quickly spread, finally reaching 
the ears of Peter the Great, who had a very weak spot in his heart for 
all sorts of curious and cunning artifices, and, naturally, it intrigued 
him greatly. His attention had been called to it back in <715 when 
travelling abroad, and it was then that he charged the celebrated dip- 
lomat A. 1. Ostermann to inspect it. The latter soon forwarded an 
oxtenshe report about the machine though he had not been able to see 
it with his own eyes. The tsar even thought of inviting Orffyreus as 
an eminent inventor to his court to take up service and asked the then 
well-known philosopher Christian Wolf to give his opinion. 

Orffyreus was showered with offers, one better than the other. Kings 
and princes bestowed munificent awards. Poets composed odes in honour 
of his wonder-wheel. But there were some who thought him a charlatan. 
The more daring openly accused him, even offering 1,000 marks to 
anyone who would come forth and expose the councillor. One lampoon 
against him gave a drawing which is reproduced in Fig. 50 and which 
provides a rather simple explanation for the mystery a cunningly 
hidden person who pulled at a rope wound round that part of the axle 
which was concealed in the pillars supporting the wheel. 

The trick was bared by chance only because the councillor had had 
a tiff with his wife and maid who had both been initiated into the 
secret. Otherwise we would probably still be guessing. It seemed that 
the notorious machine was indeed turned by a hidden person Orffyre- 
us's brother, or maid pulling at a slender cord. But the councillor 
did not lose face, persistently assuring all and sundry even on his death- 
bed that his wife and maid had maligned him out of spite. However, 
trust in him was shattered. No wonder he tried to drum into the head 
of the tsar's envoy, Schumacher, the point that human beings were full 
of malice. 

75 




Fig. 50. The secret of Orffyreus's machine. 
(From an old drawing.) 

Around the same time there also lived in Germany another renowned 
"perpetual motion" machine inventor, one Hertner. Schumacher wrote 
of his contraption the following: "Herr Hertner's perpetuum mobile, 
which I saw in Dresden, consists of tarpaulin filled with sand and a 
grinder-like machine which turns forwards and backwards by itself. 
However the inventor says it cannot be made larger." Undoubtedly 
this machine, too, gave no "perpetual motion", being at best an artfully 
contrived device with a just as artfully concealed livingbut by 
no means "perpetual motion" machine. Schumacher was right when 
he wrote to Peter the Great that French and English scholars "mock 
these perpetuum mobiles as objectionable to principles of mathematics". 



CHAPTER FIVE 

PROPERTIES OF LIQUIDS AND GASES 




THE TWO COFFEE-POTS 

Fig. 51 shows two coffee-pots of the same width. One, however, is 
taller than the other. Which of the two will hold more? An unthinking 
person would probably point to the taller one. However, we would 
be able to fill it up only to the level of its spout, and if we poured more 
in, it would all spill out Now since the spouts of both coffee-pots are 
on the same level, the lower one takes 
just as much liquid as the taller 
one does. You will easily realise why. 
The coffee-pot and its spout are two 
communicating vessels and hence 
inside both the liquid should be 
at an identical level, even though 
the liquid in the spout weighs much 
less than that in the coffee-pot 
proper. Unless the spout is high 

enough, you will never be able to fill the coffee-pot up to the top; the 
water will simply keep on spilling out. Usually the spout is even a 
bit higher than the top of the coffee-pot to enable one to incline it 
without spilling out its contents. 



IGNORANCE OF ANCIENTS 

Romans today still use what is left of the aqueducts t 
forefathers built. Though the Roman slaves of old did 
we can't say that of the Roman engineers in charge. 



Fig. 51. Which coffee-pot takes 
more? 




of elementary physics was plainly inadequate. Fig. 52 reproduces a 
picture preserved at the German Museum in Munich. As you see, 
the Romans did not sink their water systems in the ground but placed 




Fig. 52. The aqueducts of ancient Rome 

them on high supports of masonry. Why? Aren't underground pipes 
of the type we use today simpler? Roman engineers of old had a very 
hazy notion, however, of the laws of communicating vessels. They 
feared that in two reservoirs connected by a very long pipe, the 
water would not rise to the same level. Furthermore, if the pipes were 
laid in the ground and followed the natural relief, in some places the 
water would have to flow upwards, and this was something the 
Romans were afraid it would not do. That is why their aqueducts 
usually slope all along the way. They often had either to take the pipes 
on a roundabout route or erect tall arches. One Roman aqueduct, 
known as the Aqua Marcia, is 100 km long, though it is half the distance 
between its two points as the crow flies. As yon see, the ancient Romans' 
ignorance of an elementary law of physics caused 50 km of extra 
masonry to be built. 



78 



LIQUIDS PRESS ... UPWARDS 



Even people who have never studied physics know that liquids press 
down on the bottom of the vessels holding them and sideways at the 
walls. Many, however, have never suspected that liquids also press 
upwards. An ordinary lamp-glass will easily reveal this. Cut out of 
a piece of thick cardboard a disc large enough to cover the top of the 
lamp-glass. Cover the top of the glass 
with it and then dip the glass into a 
jar of water as shown in Fig. 53. To 
prevent the disc from slipping off when 
the lamp is immersed, tie a piece of 
thread to it and hold it as shown, or 
simply press it down with your finger. 
After you have dipped the glass far 
enough, you" can let the thread, or your 
finger, go. The disc will remain where it 
is, being kept in place by the water 
pressing up on it. 

If you want to, you can even gauge the 
value of this upward pressure. Carefully 
pour some water into the glass. As soon as 
the level of the water in the glass reaches 
that of the water in the jar, the disc slips 

off, because the pressure exerted by the water on the disc from below 
is offset by the pressure v exerted on it from above by the column of 
water in the glass, the height of which is equal to the depth to which 
the glass has been dipped. Such is the law concerning the pressure that 
a liquid exerts on any immersed body. This incidentally results 
in that "loss" of weight Jn liquids of which Archimedes's famous prin- 
ciple speaks. 

With the help of several lamp-glasses of different shapes but with 
tops of one and the same size you may test another law dealing with 
liquids: that the pressure a liquid exerts on the bottom of the contain- 
ing vessel depends only on the size of the bottom and the height of 




Fig.53. A simple way to demon- 

strate_tbat liquids [press up- 

waids 



79 



the "column" of liquid; it does not 
depend at all on the vessel's shape. 
This is bow you test this law. Take 
different glasses and dip them to 
one and the same depth. To see 
that no mistakes occur, first glue 
strips of paper to the glasses at equal 
heights from the bottom. The card- 
board disc you used in the first 
experiment will slip off every time 
you pour in water to the same level 
(Fig. 54). Consequently the pressure 
exerted by columns of water of 
different shapes is the same as 
long as the bottom and height are 
the same. Note that it is the height, 
and not the length, that is impor- 
tant, because .a long but inclined 
column exerts exactly the same 




Fig. 54. The pressure liquid exerts 
on the bottom of the vessel depends 
only on the area of the base and the 
liquid's height. The drawing shows 
you how to check this 



pressure on the bottom as is exerted by a shorter but perpendicular col- 
umn as high as tht inclined one provided, of course, the bottom of 
each is the same. 

WHICH IS HEAVIER? 



Place a pail of water, full up to 
the rim, on one pan of a pair of 
scales. Then put on the other 
pan another pail of water, also 
full up to the rim, but with a piece 
of wood floating in it (Fig. 55). 
Which of the two is heavier? I 
asked this of different people and 
got contradictory answers. Some 
said the pail with the piece of 
wood in it would be heavier be- 
cause it held a piece of wood in 




Fig. 55. Both pails are full to the 

rim. One has a piece of wood in it. 

Which is heavier? 



addition to the water. Others said the pail of water without the piece of 
wood would be heavier, since water generally weighs more than wood. 
Neither were right. Both pails weigh the same. The second pail, true, 
contains less water than the first one, because the wood displaces some 
of the water. But, according to the related law, every floating body 
displaces with its immersed part exactly as much liquid (in weight) as 
the whole of this body weighs. That is why the scales balance. 

Now try to solve another problem. Take a glass of water, put it on 
one of the pans, and put a weight next to it. Balance the scales. Then 
drop the weight next to the glass into it. What happens to the scales? 
According to Archimedes's principle, in the water the weight should 
weigh less than when on the pan. 

Consequently, oughtn't this pan rise? However, the pans main- 
tain their equilibrium. Why? When dropped into the glass the weight 
displaced some of the water which then rose to a level higher than 
before. This added to the pressure exerted on the bottom of the 
vessel, which thus sustained an additional force equivalent to the 
weight lost by the weight. 

A LIQUID'S NATURAL SHAPE 

We are used to thinking that liquids have no shape of their own. That 
is not true. 

The natural shape of any liquid is that of a sphere. As a rule, 
gravity prevents liquids from assuming this shape. A liquid either 
spreads in a thin layer if spilled out of a vessel, or takes the vessel's 
shape. But when inclosed in another liquid of the same specific 
weight, it, according to Archimedes's principle, "loses" its weight, 
seeming to weigh nothing; now gravity has no effect on it and it as- 
sumes its natural spherical shape. 

Since olive oil floats in water but sinks in alcohol we can mix the 
two in such proportions that the oil will neither sink nor float in this 
mixture. An odd thing happens when we drip in a little oil with the 
help of an eyedropper. The oil collects into a large round drop which 
neither floats nor sinks, but hangs suspended (Fig. 56). To get a true 
image of the sphere, you should do the experiment in a flat- walled 

62668 31 



vessel or in one of any shape but placed inside a flat-walled vessel 
full of water. 

You must do this experiment patiently and carefully, because other- 
wise you will get several smaller drops instead of a large one. Don't 
feel disheartened if it doesn't work out; even then it's sufficiently 
illuminating. 






Fie. 56. Oil inside diluted alcohol 

collects into a drop which neither 

sinks nor floats. (Plateau's experi- 

ment.) 




Fig. 57. A ring is given off when 

the oil drop in the alcohol is spun 

by means of a rod 



Let's carry this experiment further. Take a long stick or a piece of 
wire and transfix the oil drop. Start turning. The drop also participates 
in this revolution. You get still bettor results by attaching to the stick 
or wire a small cardboard disc soaked in oil and inserting it fully in 
the drop you are twirling. The spin compels the drop to compress and 
then give off a ring a few seconds later (Fig. 57). As it breaks up the 
ring creates new drops which continue to revolve round the central one. 

The Belgian physicist Plateau was the first to conduct this instruc- 
tive experiment, of which I have given you the classical description. 
It would be much easier and just as instructive to do this experi- 
ment in another way. Take a small tumbler, rinse it with water, and 
fill it with olive oil. Place it on the bottom of a larger glass. Then 
carefully pour into the glass enough alcohol to cover the tumbler. 
Gradually add a little water with the help of a spoon. Do this very 
carefully, so that the water drips down the walls of the glass. The top 
of the oil in the tumbler starts to bulge, and when enough water has 



been poured in, the oil rises up 
from the tumbler in a rather large 
drop to hang suspended in this 
mixture of alcohol and water 
(Fig. 58). 

For want of alcohol you can 
use aniline instead. Aniline is a 
liquid which is heavier than 
water at room temperature but 
lighter than water when heated to 
75-85 C. By heating up the wa- 
ter, we can make the aniline 

swim inside it and assume the form of a large drop. At room tem- 
perature you can suspend an aniline drop in a solution of table salt. 
Another convenient liquid is the dark-crimson opthotoluidine, which 
at 24 C has the same density as salt water, into which it is poured. 





Fig. 58. Plateau's experiment 
simplified 



WHY IS SHOT ROUND? 

I noted earlier that any liquid will assume its natural spherical 
shape when gravity ceases to act on it. You need only remember what 
I said before about a falling body having no weight and discount the 
negligible atmospheric resistance when a body starts to fall (raindrops 
accelerate only when they start to fall; by the second half of the first 
second the fall already becomes uniform and the drop's weight is offset 
by atmospheric resistance which grows together with the velocity of 
the falling drop) to realise that falling portions of liquid should also 
take on a spherical form. 

That is really so. Falling raindrops are indeed round in shape. Shot 
is nothing but solidified drops of molten lead which in the process 
of making are dropped from a great height into a cold water bath 
where they solidify in the shape of absolutely right spheres. Shot is 
also called "tower" shot because in its making it is dropped from the 
top of a tall "shot tower" (Fig. 59). These towers are metal structures 
45 m high. At the top they have a shot-pouring shop with boilers for 
melting the lead, and at the bottom a water bath. The ready shot is 




then graded and processed. The drop of molten lead solidifies into shot 
while falling. The water bath is needed merely to soften the impact and 

to prevent the shot from losing its spherical 
shape (shot with a diameter of more than 6 mm, 
so-called canister shot, is made differently, 
by chopping off pieces of wire, which are then 
rolled into balls). 

THE "BOTTOMLESS" WINEGLASS 

Fill a wineglass with water right up to the 
very rim. Take some pins. Do you think place 
could be found in the wineglass for a couple of 
them? Try and see. 

Throw the pins in and count them as you do. 
But be careful about it, Take the pin by its 
head and dip its point into the water. Then 
carefully let go, without pushing it or exert- 
ing any pressure, so that water is not spilled 
out. As you drop the pins in, they fall to the 
bottom, but the level of the water is the same. 
You drop in ten, then another ten, and then 
another ten. The water does not spill out. You 
can go on till there are a hundred at the 
bottom of the glass. But still no water has 
spilled out (Fig. 60). Nor, for that matter, 
has it risen to any noticeable degree above 
the rim. 

Add some more pins. Now you can even 
count them in hundreds. You may have as 
many as 400 pins in the glass, but still no wa- 
ter spills out. However, now you see that the 
surface is bulging above the rim. Therein lies 
the answer to this so far incomprehensible 
phenomenon. Water scarcely wettens glass as 
shotftower long as it is a little greased, and the rim 





of the wineglasslike all the chin a ware and 
glassware we use for that matter is sure to 
have some traces of grease which are left 
when we touch it with our fingers. And as it 
doesn't wetten the rim the water displaced 
by the pins bulges. You can't see it, but if 
you went to the pains of reckoning the vol- 
ume of one pin and of comparing it with the 
volume of the bulge above the rim of the 
wineglass you would realise that the former 
volume is hundreds of times smaller than 
the latter, which explains why a "full " wine- 
glass will still have enough room for another 
few hundred pins. 

The wider the mouth of the wineglass is, 
the more pins it can take, because there is a 
larger bulge. A rough reckoning will make the 
point clear. A pin is about 25 mm long 
and half a millimetre thick. You can easily 
reckon the volume of this cylinder by invoking the well-known 
geometrical formula (^-}\ it will be equal to 5 mm 8 . Together 
with the head, the pin will have a total volume of not more than 5.5 mm 1 . 
Let us now reckon the volume of the water in the bulge. The diameter 
of the wineglass mouth is 9 cm, or 90 mm. The area of such a circle is 
about 6,400 mm 8 . Assuming that the bulge is not more than 1 mm 
high, we thus got a volume of 6,400 mm 8 , which is 1,200 times more 
than the volume of the pin. In other words, a "full" wineglass of water 
can take more than a thousand pins. And indeed we can get the wineglass 
to take a thousand pins if we are careful enough. To the eye they seem 
to occupy the whole of the wineglass and even stick out of it. But still 
no water spills out. 

UNPLEASANT PROPERTY 

Anyone who has ever had to handle a kerosene lamp most likely 
knows what annoying surprises it can spring on one. You fill a tank with 
it and then wipe the tank dry on the outside. An hour later it's wet 



Fig. 60. How many 
pins in the wine- 
glass? 



again. You have only yourself to blame. You probably didn't screw 
on the burner tight enough, and the kerosene, trying to spread along 
the glass, seeped out. To avert such "surprises", screw the burner 
on as tight as you can. But when you do that, don't forget to see that 
the tank is not full up to the brim. When it warms up, kerosene 
expands rather considerably increasing in volume by a tenth every 
time the temperature rises by another 100. So if you don't want the 
tank to explode, you must leave some room for the kerosene to 
expand. 

The property of kerosene to seep through causes unpleasant things 
aboard ships whose engines burn kerosene or oil. When due precau- 
tions are not taken, it is absolutely impossible to use such ships to 
carry any other cargoes except kerosene or oil, because when they seep 
out through unnoticeable crevices in the tanks these liquids spread 
not only to the metal surfaces of the tanks but literally everywhere, 
even to the clothing of the passengers to which they impart a smell 
that nothing will kill. 

Attempts to fight this evil are often to no avail. Jerom K. Jerome, 
the British humorist, wasn't guilty of much of an exaggeration when 
in his Three Men in a Boat he wrote of paraffin oil, which is remarkably 
alike kerosene. 

"I never saw such a thing as paraffin oil is to ooze. We kept it in 
the nose of the boat, and, from there, it oozed down to the rudder, 
impregnating the whole boat and everything in it on its way, and it 
oozed over the river, and saturated the scenery and spoilt the atmos- 
phere. Sometimes a westerly oil wind blew, and at other times an 
easterly oil wind, and sometimes it blew a northerly oil wind, and 
maybe a southerly oil wind; but whether it came from the Arctic 
snows, or was raised in the waste of the desert sands, it came alike to 
us laden with the fragrance of paraffin oil. 

"And that oil oozed up and ruined the sunset; and as for the moon- 
beams, they positively reeked of paraffin.... 

"We left the boat by the bridge, and took a walk through the town 
to escape it, but it followed us. The whole town was full of oil." (Ac- 
tually it was only the clothing of the travellers that reeked of paraf- 
fin oil.) 

66 




The property kerosene has of wettening the outer surface of tanks 
led people to wrongly think that kerosene could ooze through metal 
and glass. 

THE UNSINKABLE COIN 

It's to be found not only in fairy tales. A few easy experiments will 
show you that such things really exist. Start with a small object a 
needle, for instance. It seems impossible to make a steel needle float, 
doesn't it? But it isn't really so hard to<do. Place a strip of cigarette 
paper on top of the water uTa glass and an absolutely dry needle on 
top of the paper. Carefully remove the cigarette paper in the following 
way. Take another needle or a pin and, 
gradually working to the middle, gently 
push the strip of paper into the water. 
When the strip is soaked through, it will 
sink, but the needle will continue to float 
(Fig. 61). By moving a magnet at water 
level from outside the glass you can even 
make the floating needle spin round. 

With a little experience, you can dispense 
with the cigarette paper entirely. All you 
need do is to take the needle by the middle 
and, holding it parallel to the water, drop 
it from a small height. You can make a pin, 
which like the needle must not be thicker 
than 2 mm, a light ^button, or some small 
metal object float in the same way. 
When you have got the knack of it, try a 
coin. 

All these metal objects float because 
water hardly wettens metal covered with 
a very thin film of grease from our hands. 
You can even see the depression a floating 
needle makes on the surface of the water. 
Trying to regain its original position, the 
surface film buoys up the needle which is 




Fig. 61. A floating needle. 
Top: a cross-section of the 
needle (2 mm thick) and 
the depression it makes (a 
twofold magnification). Bot- 
tom: how to make the nee 
die float by using a strip 
of paper 



also buoyed up by a force equal to the weight of the water displaced 
by the needle. The easiest way of making a needle float is, of course, 
to cover it with grease. Then it will never sink. 

CARRYING WATER IN A SIEVE 

Neither is this something that can be done only in a fairy tale. Phys- 
ics can help us to undertake this seemingly impossible task. Take a 
wire sieve of 15 cm across with holes not smaller than 1 mm in diameter 
and dip it into melted paraffin, to cover it with a thin, barely discern- 
ible film. 

Your sieve remains a sieve; it still has holes in it through which a 
pin can go quite freely, but now you can carry water in it even quite 
a lot of it. Only be careful when pouring the water in and see to it that 
you don't jolt the sieve while doing that. 

Why doesn't the water drip through? Failing to wetten the paraffin, 
the water forms a thin film which bulges through the holes of 
the sieve; it is this film that keeps the water from dripping through 
(Fig. 62). This waxed sieve will even float, which means that you 
can not only carry water in a sieve, but also use it as a boat. 

This seemingly paradoxical experiment explains several ordinary 
things to which we are too accustomed to ever think of why they 
are done. The tarring of barrels and boats, the greasing of corks and 
stoppers with fat, the painting of roofs with oil paint and, generally, 
the coating with oily substances of everything we want to make imper- 
vious to water, as well as the rubberising of cloth, is the same as making 
the sieve we just described, with the exception that the sieve, of course, 
seems exceedingly unusual. 



- 62. Why the sieve carries water 



FOAM HELPS ENGINEERS 



The experiment of the floating steel needle or copper coin bears 
some resemblance to a process employed in mining to "enrich" oresi 
i.e., to increase the content of the minerals in them. Engineers know 
many methods for dressing ores, but the one we have in mind and which 
is called "flotation" is best; it is successful when all other methods fail. 

Flotation consists in the following. Finely ground ore is loaded into 
a bath containing water and oily substances that inclose the mineral 
particles in a very thin film which water cannot wet. Air is then blown 
in to form a foam composed of a mul- 
titude of tiny bubbles. The greased 
particles of the mineral attach them- 
selves to the air bubbles and rise 
up with them much in the same way 
as an air balloon lifts a gondola 
(Fig. 63). The particles of ore gangue 
that have no grease envelope cannot 
attach themselves to the air bubbles 
and sink. Note that the air bubbles 
in the foam are much bigger than 
the particles they carry and are well 
able to lift the solid speck up. As 
a result, nearly all the particles of 

the mineral are floated on top in the foam which is skimmed off 
for further processing, during which the so-called concentrated ore 
which is dozens of times richer in content than the original ore is 
separated. Flotation techniques are so well elaborated that a judicious 
choice of reagents will separate the mineral from the ore gangue in 
every particular case. 

Incidentally, we ha\e a chance accident, and no theory, to thank 
for the flotation method. One day, at the end of the past century, Carrie 
Everson, an American schoolmistress, was washing greasy sacks that 
had been used to stack copper pyrites. She happened to notice that the 
pyrite particles left in the sacks floated together with the lather. 
It was this that suggested the flotation method. 




Fig. 63. The essence of flota- 
tion 



FAKE "PERPETUAL MOTION" MACHINE 

You will sometimes find the following contraption (Fig. 64) 
described as a genuine "perpetual motion" machine. Oil (or water) 
poured into a vessel is soaked up by wicks at first into one vessel and 
then by more wicks into another vessel still higher up. The top \essel 
has a grooved outlet through which the oil pours onto a paddle wheel, 
causing it to turn. From the bottom tank the oil is again soaked up 
by wicks to the top. Thus, the oil supposedly never stops pouring onto 
the paddle wheel, making the wheel turn for ever and ever. 




Fig. 64. Non-existent "perpetual motion" machine 

If the people who described this thing were to take the pains to make 
it, they would realise that not a single drop of oil would ever reach 
the upper vessel, let alone make the wheel go. Incidentally, we don't 
necessarily have to make this contraption to realise that this is so. 
Indeed, why should the inventor think the oil should necessarily flow 
off the upper bent portion of the wick? It is quite true that capillary 
forces, having overcome gravity, lift the oil up the wick. But it is these 
same forces that prevent the oil in the pores of the soaked wick from 
oozing off. Even supposing for a moment that the oil will reach the 
upper vessel of our fake "perpetual motion" machine due to capillary 
forces, we shall have to admit that the same wicks which supposedly 
lift the oil up would themselves lower it to the bottom tank. 

The contraption we have just mentioned resembles another water- 

90 



driven one, invented by the Italian mechanic S trad a the Elder way 
back in 1575. Fig. 65 shows you this amusing device. As it turns, 
an Archimedes's screw lifts water to the upper tank, from which it pours 
out through a groove to strike at the paddles of the tank-filling wheel 




Fig. 65. An ancient design of a water-driven "perpetual motion" 
machine to turn a grinding stone 

shown in the bottom right-hand corner. This wheel turns a grinder 
and simultaneously operates by means of several gears the same Ar- 
chimedes's screw which lifts the water to the upper tank. To make a 
long story short, the screw turns the wheel and the wheel turns the 

91 



screw! If such contraptions were possible, the simplest thing would 
be to throw a rope over a pulley and tie identical weights to each end. 
As one weight fell it would lift the other one, which, dropping in turn, 
would lift the first one. Wouldn't that be a fine "perpetual motion" 

machine? 

BLOWING SOAP BUBBLES 

Do you know how to blow soap bubbles? It is not so simple as it seems. 
I, too, thought there was nothing particular in it until I saw for myself 
that the ability to blow big beautiful bubbles is in its way an art that 
needs some experience. But is it really worth while doing such a seem- 
ingly silly thing as blowing soap bubbles? After all, they have won 
a rather bad reputation among the laymen. Physicists have other 
views, however. "Blow a soap bubble, " said the great British physicist 
Kelvin, "and observe it. You may study it all your life, and draw one 
lesson after another in physics from it. " 

Indeed, that magic iridescence on the slimmest of soap films en- 
ables the physicist to gauge the length of light waves, while a study of 
the tension of these gossamer films helps him to formulate the laws 
governing the interaction of forces between particles those self-same 
forces of cohesion without which the world would be but a cloud of 
the finest dust. 

The few experiments described below do not have such serious aims; 
they are given simply to provide instructive entertainment and to 
teach you how to blow soap bubbles. In his book Soap Bubbles and 
the Forces Which Mould Them, the British physicist Charles Boys 
describes at length many different experiments that one can stage 
with these bubbles. So if you are interested in them, let me refer you 
to this wonderful book. 

Below you will find only a few of the simplest experiments. Ordi- 
nary laundry soap will do toilet soaps are less suitable for the pur- 
pose. But you can also use pure olive-oil or almond-oil soap, which is 
best for obtaining large and beautiful bubbles. Carefully dissolve a 
cake of soap in pure cold water till you get a rather thick lather. Pure 
rain water or melted snow is best but you may use cooled boiled water 
instead. To prolong the life of the bubbles Plateau suggests adding 
glycerin to the lather in a mixture of one part to every three. Skim the 

92 



froth and the small bubbles off with a spoon and then dip in the lather 
a slender clay pipe, with its end preliminarily soaped both on the inside 
and outside. Good results can be achieved also by using straws of 
about 10 cm long, that are split at the bottom in the form of a cross. 
This is how you blow the bubble. Dip the pipe into the lather, hold- 
ing it vertically so that it becomes covered with film. Then gently 
blow at the other end. As the bubble is filled with warm air from our 
lungs which is lighter than the air in the room it will float up at 
once as long as you can blow a bubble of some 10 cm across; otherwise 
you must add more soap until you can blow bubbles of this diameter. 
This alone is not enough; there is another test that you must make. 
After you blow the bubble, dip your finger in the lather and try to 
pierce the bubble with it. If it doesn't burst you can start experiment- 
ing. If it does add a little more soap. Do the experiments slowly, 
with care, and without undue haste. The room must be well lit; other- 
wise the proper iridescence will be lacking. Now for a few entertaining 
experiments. 






Fig. 66. Soap bubbles 



1) A flower in a bubble. Pour the lather three millimetres deep into 
a plate or tray. Then place a flower or a little vase in the middle and 
cover it with a glass funnel. Slowly lift the funnel, blowing meanwhile 
in its narrow end to get a soap bubble. When the bubble is large enough, 
tilt the funnel as shown in Fig. 66 and release the bubble. Your 
flower or vase will be under a transparent, semicircular, iridescent 
soap bubble. You can take a statuette instead of a flower and crown 
it with a small soap bubble as shown in Fig. 66. To get the smaller 
bubble, you must spill a little lather on top of the statuette before 
you blow the big bubble. Then pierce the big bubble with a pipe and 
blow out the small bubble inside. 

2) A nest of bubbles (Fig. 66). Take the funnel you used for the pre- 
vious experiment and blow a large bubble as you did before. Then take 
a straw and dip it into the lather, leaving only the very end, which 
you blow through, dry. Gently pierce the wall of the first bubble till 
you get to the middle. Then slowly draw the straw back without bring- 
ing it out, and blow out a second bubble inside the first. Repeat 
to get a third bubble inside the second, a fourth inside the third, and 
so on. 

3) A cylindrical bubble (Fig. 67). For this purpose you must have 
two wire rings. Blow an ordinary round bubble onto one of them, the 
lower one. Then take the second ring, wet it and attach it to the top 

of the bubble. Lift it until the bubble as- 
sumes a cylindrical shape. Note that if you 
lift the upper ring to a height more than the 
ring's circumference, half of the cylinder 
will contract and the other half will bulge 
until the bubble divides into two. 

The film of the soap bubble, which is con- 
tinually in a state of tension, presses on the 
enclosed air; by directing the narrow end of 
the funnel at the flame of a candle you will 
see that the strength of this very thin film is 
not so negligible as you might think the 
flame wavers quite noticeably (Fig. 68). 

It is interesting to observe a bubble float* 




Fig. 67. How to make 
a cylindrical soap bub- 
ble 



ing out of a warm room into a cold 
one. It shrinks noticeably. On the other 
hand, it expands when brought from a 
cold room into a warm one. This, natu- 
rally, depends on the contraction and 
expansion of the air inside. If you were 
to blow a bubble of 1,000 cm 8 in a sub- 
zero frost of 15 C and then bring it into 
a room where the temperature is 15 C 
above zero, it would increase in volume 

by rouprhly 110 cm 3 (I,000x30x-^p). Ifff^ 

I must note that a soap bubble is not 
always as short-lived as is usually 
thought. When handled with care it can 
be preserved for some ten days, if not 
more. The British physicist Dewar, who 
won fame for his studies of the liquefac- 
tion of air, preserved soap bubbles in special bottles, well shielded 
from dust, dryness, and shock, and was able to keep some bubbles for 
a month and more. The American Lawrence kept soap bubbles under 
a bell-glass for years on end. 




Fig. 68. The air forced out by 

the walls of the soap bubble 

causes the candle-flame to 

waver 



THINNEST OF ALL 

Few probably know that the film of a soap bubble is one of the thin- 
nest things you can sec with the unaided eye. The customary compar- 
isons we draw upon to express thinness are very thick compared with 
the film of a soap bubble. A thing "as thin as a hair" or "as thin as 
cigarette paper" is very thick compared with the walls of a soap bubble, 
which are 5,000 times thinner than a hair or cigarette paper. A human 
hair magnified 200 times is about a centimetre thick. If we magnified 
the cross-section of the film of a soap bubble the same number of times, 
wo still wouldn't be able to see it. We would ha\e to magnify it another 
200 times to see it as a slender line. Then a hair magnified 40,000 times 
would be more than two metres thick. Fig. 69 well illustrates this. 



95 




n mm 



Fig. 69. Top: the eye of a neodle, a human hair, germs, and 

a spiderweb magnified two hundred times. Bottom: germs and 

the wall of a soap bubble magnified 40,000 times 



WITHOUT WETTING A FINGER 

Take a largo plate and put a coin on it. Then add enough water to 
cover the coin. Ask your guests to pick up the coin without wetting a 
finger. It seems impossible, doesn't it? 

But it can be solved in a very simple way with the aid of a glass 
and some paper. Take a piece of paper, light it and, while it is still 
burning, place it inside the glass. Then quickly put the glass down, 
bottom up, on the plate. The paper goes out, the glass fills with white 
wisps of smoke and all the water in the plate flows under it. The coin 
will naturally remain where it is. A minute or two later, as soon as 
the coin is dry, you can pick it up without wetting a finger. 

What sucked the water under the glass and maintained it there 
at a certain level? Atmospheric 
pressure. The burning paper heated 
the air in the glass, increased its 
pressure and part of it leaked out. 
When the paper went out the air 
cooled again, and its pressure de- 
creased. The pressure of the air 
outside the glass forced the water 
in the plate under the glass. Instead 

of paper you may use matches stuck '*' J^S"^*^ %* 
in a cork as shown in Fig. 70. 

There is current a wrong explanation of this very old experiment 
(it was first described and properly explained by the physicist Philo 
of Byzantium who lived somewhere in the 1st century B.C.). Some people 
say that the water flows under the glass because it is "oxygen that burns 
out", and that is why the amount of gas in the glass diminishes. This is 
absolutely wrong. The water flows under the glass only because the air 
is heated and not at all because any oxygen is absorbed by the burning 
paper. You can check this statement in the following way. Heat 
up the glass by pouring boiling water into it, thus dispensing with 
the burning piece of paper. Then, if you take instead of paper a piece 
of cotton wool soaked in alcohol, which burns longer and heats up 
the air better, the water will rise up to almost the middle of the glass; 

72668 97 




note that oxygen comprises only a fifth of the air in volume. Note, 
finally, that instead of the allegedly "consumed" oxygen, you have 
carbon dioxide and water vapour. While the first dissolves in water, 
vapour remains, replacing part of the oxygen. 

HOW WE DRINK 

Can this pose a problem? It can. When drinking we bring a glass or 
a spoonful of liquid up to our lips and suck in the contents. It is this 
simple thing we are so used to, that we have to explain. Indeed why 
does the liquid rush into our mouth? What makes it do that? When 
we drink, our chest expands, thus rarefying the air in our month. The 
pressure of the outer air forces the liquid to rush into the place where 
pressure is less; so does it find itself in the mouth. Liquids in commu- 
nicating vessels would behave in exactly the same way were we to 
rarefy the air above one of them. Atmospheric pressure would compel 
the liquid in this particular vessel to rise. If you enclose the mouth of 
a bottle with your lips you will fail to suck in the water as the pres- 
sure of the air in your mouth and above the water will be the same. 
So, strictly speaking, wo drink not only with our mouths, but also 
with out lungs, since it is chest expansion that makes the liquid rush 
into our mouths. 

A BETTER FUNNEL 

Those who have ever poured liquids into a bottle through a funnel 
know that from time to time you have to lift the funnel a little because 
otherwise the liquid will stay in it. This is because the air in the bottle 
fails to find an outlet and so blocks up the liquid in the funnel. A little 
of the liquid will drip in so that the air in the bottle is slightly com- 
pressed by the liquid's pressure. However, the cramped air will become 
resilient enough to offset the weight of the liquid in the funnel by its 
own pressure. By lifting the funnel, we give the compressed air a chance 
to escape. Then the liquid begins to flow in again. So, to make a 
better funnel, the narrower part should have ridges outside to prevent 
the funnel from fitting tightly in the mouth of the bottle. 



A TON OF WOOD AND A TON OF IRON 

What is heaviera ton of wood or a ton of iron? Some heedlessly 
answer that the ton of iron is heavier, thus raising a laugh at their 
expense. The questioner would probably laugh still louder were he 
told that the ton of wood is heavier. This seems absolutely incredible, 
but it is true, strictly speaking. 

The point is that Arcbimedes's principle can be applied not only 
to liquids but also to gases In the air, every object "loses " in weight 
as much as the volume of displaced air weighs. Wood and iron also 
lose a part of their weight, and to get their true weight, you must add 
the loss. Consequently, the true weight of the wood in our case is one 
ton plus the weight of the air it displaces. 

The true weight of the iron is also one ton plus the weight of the air 
that the iron displaces. However, a ton of wood occupies a much larger 
space about 15 times more than a ton of iron. Hence, the true weight 
of a ton of wood is more than that of a ton of iron. Rather should we 
say that the true weight of the amount of wood which weighs a ton 
in the air is more than the true weight of iron which also weighs a ton 
in the air. 

Since a ton of iron occupies a volume of 1/8 m 8 and a ton of wood 
a volume of about 2 m 8 , the difference in the weight of the displaced 
air should be about 2.5 kg. It is by this amount that a ton of wood is 
really heavier than a ton of iron. 

THE MAN WHO WEIGHED NOTHING 

To be as light as a feather incidentally, in spite of the popular 
notion, a feather is really hundreds of times heavier than air, and only 
hovers because due to its rather great "wing-spread " the atmospheric 
resistance it encounters is much greater than its weight and even 
lighter than air, to rid oneself of the fetters of gravity and freely soar 
into the skies, has boon the dream of many a child and even grown-up; 
But they forget that they can walk around with ease only because they 
are heavier than air. ' 

"We live at the bottom of an ocean of air," Torricelli once said. 
If we were suddenly to grow a thousand times lighter, lighter than air, 

7* 99 



we would inevitably float up to the top of this ocean of air. We would 
rise miles up until we reached regions where the density of the rare- 
fied air would be the same as that of our body. Our dream of hovering 
in free flight above the hills and vales would be shattered; we would 
have freed ourselves of gravity but would have been captured by other 
forces those of the air currents. 

H. G. Wells tells a story in which a very fat man wanted to rid him- 
self of his fatness. The person who tells the story was the possessor 
of the recipe of a miraculous brew which could rid people of excessive 
weight. The fat man made the brew according to the recipe and drank 
it. And this is what happened. 

"For a long time the door didn't open. 

"I heard the key turn. Then Pyecraft's voice said, 'Come in.' 

"I turned the handle and 
opened the door. Naturally I ex- 
pected to see Pyecraft. 

"Well, you know, he wasn't 
there! 

"I never had such a shock in 
my life. There was his sitting- 
room in a state of untidy disor- 
der, plates and dishes among the 
books and writing things, and 
several chairs overturned, but 
Pyecraft 

"'It's all right, o'man; shut 
the door," he said, and then I 
discovered him. 

"There he was right up close 
to the cornice in the corner by 
the door, as though someone had 
glued him to the ceiling. His 
face was anxious and angry. He 
panted and gesticulated. 'Shut 
the door/ he said. 'If that wom- 
an gets hold of it' 




Pig. 71. "There he was right up 
close to the cornice" 



"I shut the door, and went and stood away from him and stared. 

"'If anything gives way and you tumble down, 9 I said, 'you'll break 
your neck, Pyecraft.' 

"'I wish I could/ he wheezed. 

"'A man of your age and weight getting up to kiddish gymnas- 
tics' 

"'Don't,' he said, and looked agonised. 

"Til tell you,' he said, and gesticulated. 

"'How the deuce,' said I, 'are you holding on up there?' 

"And then abruptly I realised that he was not holding on at all, 
that he was floating up there just as a gas-filled bladder might have 
floated in the same position. He began a struggle to thrust himself 
away from the ceiling and to clamber down the wall to me. 'It's that 
prescription,' he panted, as he did so. 'Your great-gran ' 

"He took hold of a framed engraving rather carelessly as he spoke 
and it gave way, and he flew back to the ceiling again, while the pic- 
ture smashed on the sofa. Bump he went against the ceiling, and I 
knew then why he was all over white on the more salient curves and 
angles of his person. He tried again more carefully, coming down by 
way of the mantel. 

"It was really a most extraordinary spectacle, that great, fat, apop- 
lectic-looking man upside down and trying to get from the ceiling 
to the floor. 'That prescription,' he said. 'Too successful.' 

"'How?' 

"'Loss of weight almost complete.' 

"And then, of course, I understood. 

"'By Jove, Pyecraft,' said I, 'what you wanted was a cure for fat* 
nessl But you always called it weight. You would call it weight.' 

"Somehow I was extremely delighted. I quite liked Pyecraft for 
the time. 'Let me help you!' I said, and took his hand and pulled 
him down. He kicked about, trying to get foothold somewhere. It waa 
very like holding a flag on a windy day. 

"'That table,' he said pointing, 'is solid mahogany and very heavy. 
If you can put me under that' 

"I did, and there he wallowed about like a captive balloon, while 
I stood on his hearthrug and talked to him. 

101 



." ...'There's one thing pretty evident,' I said, 'that you mustn't 
do. If you go, out of doors you'll go up and up....' 

" ...I suggested he should adapt himself to his new conditions. 
So we came to the really sensible part of the business. I suggested that 
it would not be difficult for him to learn to walk about on the ceiling 
with his hands 

'"I can't sleep,' he said. 

"But that was no great difficulty. It was quite possible, I pointed 
out, to make a shake-up under a wire mattress, fasten the under things 
on with tapes, and have a blanket, sheet, and coverlet to button at the 
side. He would have to confide in his housekeeper, I said; and after 
some squabbling he agreed to that. (Afterwards it was quite delight- 
ful to see the beautifully matter-of-fact way with which the good lady 
took all these amazing inversions.) He could have a library ladder 
in his room, and all his meals could be laid on the top of his bookcase. 
We also hit on an ingenious device by which ho could get to the floor 
whenever he wanted, which was simply to put the British Encyclopaedia 
(tenth edition) on the top of his open shelves. He just pulled out a 
couple of volumes and held on, and down he came. And we agreed there 
must be iron staples along the skirting, so that he could cling to those 
whenever he wanted to get about the room on the lower level.... 
(Then, you know, my fatal ingenuity got the better of me.) I was 
sitting by his fire drinking his whisky, and he was up in his favourite 
corner by the cornice, tacking a Turkey carpet to the ceiling, when 
the idea struck me. 'By Jove, Pyecraftl' I said, 'all this is totally 
unnecessary.' 

"And before I could calculate the complete consequences of my no- 
tion I blurted it out. 'Lead underclothing,' said I, and the mischief 
was done. 

"Pyecraft received the thing almost in tears. 'To be right ways up 
again ' he said. 

"I gave him the whole secret before I saw where it would take me. 
'Buy sheet lead,' I said, 'stamp it into discs. Sew 'em all over your 
underclothes until you have enough. Have lead-soled boots, carry a 
bag of solid lead, and the thing te donel Instead of being a prisoner 
here you may go abroad again, Pyecraft; you may travel' 

102 



"A still happier idea came to me. 'You need never fear a shipwreck. 
All you need do is just slip off some or all of your clothes, take the 
necessary amount of luggage in your hand, and float up in the 
air-'" 

At first glance this all seems quite in conformity with the laws of 
physics. But objections can be made. Firstly, even if Pyecraft had lost 
his weight, he wouldn't have risen up to the ceiling at all. Recall Ar- 
ch imedes's principle. Pyecraft should have "floated "up to the ceiling 
only if his clothes and everything in his pockets would have weighed less 
than the air displaced by his fat body. We can easily reckon the weight 
of this volume of the air. We weigh almost the same as a similar volume 
of water some 60 kg. Air of the usual density is 770 times lighter 
than water, so the amount we would displace would weigh only 80 gr. 
However fat Mr. Pyecraft was, he could have scarcely weighed much 
more than 100 kg; consequently, he must have displaced not more 
than 130 gr of air. There is no question that Pyecraft's suit, shoes, 
watch, wallet and all his other belongings weighed more. In that case 
the fat man should have remained on the floor. He would have felt 
rather shaky, true, but he certainly would not have "ballooned " up 
to the ceiling. That would have happened only if he had been stark 
naked. Dressed, he must have boon like a man tied to a bouncing 
balloon. A small effort, a little jump and he would be up in the air, to 
smoothly descend again, provided, of course, there was no wind. (See 
Chapter 4 of my Mechanics for Entertainment for more about bounc- 
ing balloons.) 

"PERPETUAL" CLOCK 

You already know a few things about "perpetual motion" machines 
and of the futility of trying to invent them. Let me now tell you about 
what I shall call a "gift-power" machine, as it can work indefinitely 
without human interference, drawing its motive power from the inex- 
haustible sources of energy in nature. Everybody has most likely 
seen a barometer, a mercury or aneroid one. In the first one the mer- 
cury rises or falls depending on the changes in atmospheric pressure. 
And it is atmospheric pressure again that causes the arrow to swing 
in the aneroid barometer. 

103 



One 18th-century inventor availed himself of this arrangement to 
produce a self-winding clock that would never stop. The well-known 

British mechanic and astronomer James Fer- 
guson saw it in 1774 and this is how he de- 
scribes it. "I saw this clock, " he says, "which 
is made to go without stopping by the endless 
rising and falling of the mercury in a curious- 
ly arranged barometer. We have no reason 
to think that the clock would ever stop as 
the accumulated motive power is enough to 
make it go for a whole year, even if the ba- 
rometer were removed. To be frank, I must 
say that this clock which I examined in detail 
is the cleverest mechanism I have ever seen, 
both in design and execution. " 

Unfortunately the clock was stolen and 
nobody knows what has become of it. Luckily 
enough, Ferguson made some drawings of it, 
so it can be reproduced. 

Its mechanism consists of a large mercurial 
barometer, which has about 150 kg of mer- 
cury in two glass vessels, one with its mouth 
in the other, and both suspended in a frame. 
Both vessels move separately; when atmos- 
pheric pressure rises an ingenious system of 
levers lowers the top vessel and lifts the bot- 
tom one. When atmospheric pressure falls, 
the reverse takes place. This compels a small 
gear-wheel to turn always in one and the same 
direction. It doesn't turn only when the at- 
mospheric pressure is steady. However, in 
these intervals the clockwork is operated by 
the accumulated potential energy. And though 
it isn't easy to make the weights rise simul- 

o * < Qti. * taneously and wind the spring when they drop, 
rig. 72. An loin-century , ,. * 1 1 i_ 

"gift-power" machine the watchmakers of old were ingenious enough. 




It even happened that the energy produced by the changes in atmospheric 
pressure was far more than was needed, causing the weights to rise 
before they had managed to drop to the bottom. So a special device had 
to be made to switch off the weights at regular intervals, when they had 
gone up all the way. 

The fundamental difference between such "gift-power" machines and 
"perpetual motion" machines is obvious. Energy is not produced out of 
nothing which was what the inventors of the "perpetual motion" 
machines sought to achieve. It is supplied from an outside source in 
our particular case, the surrounding atmosphere where it is stored up 
by sunlight. To all practical intents a "gift-power" machine would 
give the same advantage as could be derived from a "perpetual motion" 
one if ever invented were it not so costly, as it is in most cases. 

Later I shall deal with other kinds of "gift-power" machines arid shall 
illustrate why such things are absolutely unprofitable commercially. 



CHAPTER SIX 

HEAT 

WHEN IS THE OKTYABRSKAYA RAILWAY LONGER? 

When asked how long the Oktyabrskaya Railway is one person gave 
this answer: "It's 640 km on the average. But in summer it's about 300 m 
longer than in winter. " 

Now this is not so absurd as it may seem. If we meant by the length 
of a railway the length of its rails, it should indeed be longer in summer 
than in winter. Don't forget that heat causes steel rails to expand by 
more than 100,000th of their length to every one degree Centigrade. 
On a blazing summer day the temperature of rails might reach 30-40C 
and more. Sometimes rails are so hot that they burn the hand. In winter 
rails may cool down to 25 C below zero and even lower. Supposing that 
the summer-winter difference in temperature is 55; by multiplying the 
railway's total length (640 km) by 0.00001 and again by 55, we get about 
a third of a kilometre. So in summer the Moscow-Leningrad railway is 
indeed the third of a kilometre, i. e., roughly 300 m, longer than in 
winter. 

It is, of course, not the length of the railway that changes but merely 
the sum-total of the lengths of all the rails. This is not one and the same 
thing, because the rails of a railway track do not d irectly^abut one anoth- 
er. Small spaces are left between their joints for the rails to freely ex- 
pand when they heat up. (This gap in the case of 8-metre rails should 
be 6 mm at zero. To fully bridge it by expansion the temperature of the 
rails should rise by 65 C. For certain technical reasons we cannot leave 
gaps in tramway rails. Usually the rails don't curve, because they are 
sunk in the ground, temperature fluctuation is not so great and the 
method used to spike the rails prevents them from curving. However, 
on a very hot day tram rails do curve, as Fig. 73, the reproduction of 
an actual photograph, well illustrates. Sometimes the same thing hap* 

106 




Fig. 73. Tram rails bend on very hot days 

pens to the rails of a railway track. On downgrades the train pulls at the 
rails sometimes even together with the sleepers. As a result, the gaps 
often disappear on such sections and the rails directly abut one another.) 
The calculation we have made shows that the total length of all the 
rails increases at the expense of the total length of these gaps; on a hot 
summer day the total length in our particular case is 300 metres more 
than in a winter frost. So to sum up: the rails of the Oktyabrskaya 
Kailway are indeed 300 m longer in summer than in winter. 

UNPUNISHED THEFT 

On the Moscow-Leningrad line several hundred metres 
phone and telegraph wire vanish without trace every 
is ever worried; all know who the culprit is. I supp 




guessed by now. The thief, of course, is the frost. What is true for rails 
is true for wire too. The only difference is that copper telephone wires 
expand 1.5 times more than steel, when heated. And since we have no 
gaps here we can really say, without any reservations whatsoever, that 
in winter the Moscow-Leningrad telephone line is indeed 500 m shorter 
than in summer. Every winter the frost steals nearly half a kilometre of 
wire and gets away with it! But it doesn't disrupt telephone or tele- 
graph communications. All that is stolen is dutifully refunded when 
warmer days set in. 

But when bridges, not wires, contract due to frosts the consequences 
are pretty bad. Newspapers had this to report in December 1927: 
"The unusual frosts France has been having lately have seriously dam- 
aged the bridge across the Seine in the heart of Paris. Due to frosts the 
bridge's steel framework contracted, causing the road blocks to fly out. 
The bridge has been temporarily closed to traffic. " 

HOW HIGH IS THE EIFFEL TOWER? 

If I were to ask you now how high the Eiffel Tower is, before saying 
"300 metres", you would probably want to know in what weather cold 
or warm? After all, the height of such an enormous steel structure could 
not be the same at all temperatures. We know that a steel rod 300 m 
long expands by 3 mm when heated by 1 C. The height of the Eiffel 
Tower should increase by roughly the same amount when the tempera- 
ture rises by 1. In warm sunny weather the steel framework of the 
tower might warm up in Paris to 40 G above zero, whereas on a cold 
rainy day its temperature might fall to 10C and in winter down to 
zero and even to as much as 10 below (heavy frosts are rare in Paris). 
The temperature fluctuation is as much as 40 and more. This means 
that the height of the Eiffel Tower may be 3 X 40=120 mm=12 cm 
more or less. 

Direct measurement has disclosed that the Eiffel Tower is still more 
sensitive to temperature fluctuations than the air itself. It warms up 
and cools quicker and reacts sooner to the sun's sudden appearance on 
a cloudy day. The changes in the height of the Eiffel Tower were detected 
by using a wire made of a special nickel steel on whose length tem- 

108 



perature fluctuations have practically no effect. This wonderful alloy 
is called invar from the word invariable. 

So, on a hot day the Eiffel Tower is taller than on a cold day by a 
bit equal to 12 cm and made of iron, which, incidentally, doesn't 
cost a sou. 

FROM TEA GLASS TO WATER GAUGE 

Before pouring tea into a glass, the experienced housewife puts in 
a tea spoon, especially a silver one, to prevent the glass from cracking. 
Practice has suggested the proper solution. 

But what is its basic principle? Why does hot water crack a tea glass? 

Because of the uneven expansion of the glass. When you pour hot 
water into a glass, not all its walls warm up at once. At "first the inner 
layer warms up, the outer one remaining cold. The heated inner layer 
expands at once. Meanwhile, since the outer one does not expand, it 
feels a strong pressure from inside. It snaps and the glass breaks. 

Don't think you can safeguard yourself against this by using thick- 
walled glasses. They, on the contrary, are liable to crack sooner than 
thin-walled ones. This is because a thin wall heats up faster and its 
temperature and expansion even out sooner. A thick-walled glass, on 
the other hand, warms up slowly. 

One thing you mustn't forget when buying thin-walled glassware- 
make sure that the bottom of the glass is thin too, because it is the 
bottom that chiefly heats up. A thick-bottomed glass will crack, however 
thin its walls. So do glasses and china cups with thick-rimmed bottoms. 

The thinner-walled a glass vessel is, the safer it is for heating. Chem- 
ists use very thin-walled vessels in which they boil water right over 
the burner. 

The ideal vessel is one that wouldn't expand at all when heated. 
Quartz almost has this property: it expands 15-20 times less than glass. 
A thick-walled vessel of transparent quartz will never crack when heated, 
even if immersed red-hot in a bath of ice (vessels of quartz are good for 
laboratory work because it melts only at 1,700C). This is also partially 
because quartz conducts heat much better than glass. 

Tea glasses crack not only when warmed up quickly but also when 
cooled quickly. Now it is uneven contraction that is to blame. As it 

109 



cools, the outer layer contracts and exerts a strong pressure on the inner 
layer, which has not cooled and contracted yet. A prudent housewife 
should not put a jar of hot jam out in the cold or into cold water. 

But back to the tea spoon. How does it protect the glass from crack- 
ing? The difference in the expansion of the inner and outer layers is 
great only when very hot water is poured into the glass at once. Warm 
water, however, doesn't make glasses crack. What happens when you 
put a tea spoon in? A it pours in, the hot water loses part of its heat to 
the metal spoon, which is, contrary to glass, a good conductor of heat. 
Its temperature drops and it becomes almost harmless, because now it 
is only warm. Meanwhile the glass has warmed up and more hot water 
won't crack it. 

In a nutshell, a metal tea spoon, especially a heavy one, offsets the 
uneven heating of the glass and prevents it from cracking. 

But why is a silver spoon still better? Because silver is a very good 
conductor of heat. It can take away the heat from the water sooner than a 
copper spoon. A silver spoon in a glass of hot tea burns the fingers. Since 
a copper spoon doesn't do that, you can easily tell the material the 
spoon is made of. 

The uneven expansion of glass walls is a menace not only to tea 
glasses but also to very important elements of boilers the water 
gauges which give the height of the water in the boiler. As the hot steam 
and water heat them up, their inner layers they are tubes of glass ex- 
pand more than thoir outer layers. Add to this the great pressure exerted 
in the tubes by the steam and water, and you will realise why they may 
so easily burst. To prevent this, they are sometimes made of two layers 
of different kinds of glass, the inner one having a smaller expansion 
factor than the outer one. 



THE BOOT IN THE BATHHOUSE 

"Why in winter is the day short and the night long, and in summer 
the other way round? The winter day is short because like all other 
visible and invisible things it contracts due to cold; meanwhile the 
night expands it is warmed up when lights and lamps are lit." How 
comically silly this "explanation", afforded by Chekhov's retired Don 

110 



Cossack sergeant, is. However, people who ridicule such "learned" 
reasoning sometimes father theories which are just as stupid. Have you 
ever heard the story of the boot which won't go on in the bathhouse 
because "the heated foot has grown larger'? A classical instance, but 
with a totally wrong explanation. 

In the first place one's temperature hardly rises at all when one is 
in a bathhouse never by more than one degree Centigrade. Only a 
Turkish bath will make it go up two degrees. Our body successfully 
resists the surrounding heat, maintaining its temperature at a definite 
level. Furthermore, this "rise" in our body temperature increases the 
volume of our body by such a negligible fraction that one doesn't no- 
tice it when drawing on a boot. The expansion factor of our bones and 
flesh is never more than a few ten-thousandths. Consequently, the sole 
and the instep could bulge only by a hundredth of a centimetre -no 
more. Boots and shoes are never sewn with such accuracy. After 
all, a hundredth of a centimetre is but the thickness of a hair! 

Still it remains a fact that it is hard to draw a boot on after a hot bath. 
However, this is not because our foot expands due to heat but be- 
cause the blood rushes to the foot, the skin swells, is damp, and grows 
tender in a word, because of things that have nothing at all in com- 
mon with expansion due to heat. 

HOW TO WORK MIRACLES 

Hero of Alexandria, the ancient Greek mathematician who invented 
the fountain that bears his name, has left the description of two artful 
methods which enabled Egyptian priests to take in worshippers by 
their "miracles". 

Fig. 74 shows one such device consisting of a hollow metal altar which 
stood in front of the temple doors, and of the mechanism, hidden be- 
neath the flagstones, that caused the temple doors to open. When in- 
cense was burned, the heated air inside the hollow altar exerted a great- 
er pressure on the water in the vessel hidden below the floor, thus 
causing it to flow through a pipe into a pail which lowered and set in 
motion the door- opening mechanism (Fig. 75). The worshippers saw, 
of course, what they thought to be a "miracle "the temple doors swung 

111 




Fig. 74. Egyptian temple "miracle" explained. The doors open when 
incense is burned on the a liar 




Fig. 75. Diagram showing how the 
temple doors swing open. (Compare 
with Fig. 74.) 




Fig. 76. Another fake miracle of 

the ancient priests. How incense 

"everlastingly" drips into the 

sacrificial flame 



open of their own accord as soon as incense and prayers were offered by 
the priests. They, naturally, knew nothing of the hidden mechanism. 
Another fake "miracle "which the priests staged is shown in Fig. 76. 
As soon as incense is burned the expanding air forces more of it to flow 
out of the cistern below the floor into pipes concealed inside the figures 
of the priests. The worshippers beheld the "miracle " of an undying 
flame. However, when the priest in charge considered the offerings too 
scanty, he unnoticeably removed the stopper in the lid of the cistern. 
This stopped the flow of incense, because now the superfluous air could 
find a free outlet. 

SELF-WINDING CLOCK 

At the close of the previous chapter I described a self-winding clock; 
its working principle was based on the changes in atmospheric pressure. 
Now I shall tell you about similar self-winding clocks, the principle 
of which is based on heat expansion. Fig. 77 depicts the mechanism of 
one of them. The central element 
consists of rods Z x and Z 2 which 
are made of a special alloy with a 
considerable coefficient of expan- 
sion. Upon expansion rod Z x engages 
the teeth of wheel X, turning it. 
Upon contraction, on the other 
hand, rod Z 2 engages the teeth of 
the wheel Y, turning it in the same 
direction. Both wheels are set on 
shaft W l which also revolves a large 
wheel with scoops on it. These 
scoops lift the mercury from the 
lower inclined tank R to an- 
other contrarily-inclined tray /? a 

down which it flows towards the left-hand wheel also with scoops. 
As these scoops fill, the wheel turns, setting in motion chain KK, 
looped around wheel K l , which is set on the same shaft W 2 as the 
big wheel, and around wheel K* which winds up the clock. Meanwhile 
the scoops of the left-hand wheel spill out the mercury into the inclined 




V/M///////////A 



Fig. 77. Diagram of a self-winding 
clock 



82668 



113 



tank R l9 down which it flows to reach the right-hand wheel, and the 
cycle begins all over again. 

This clock, apparently, would go on ticking, while rods Z 1 and Z a 
expand and contract. All we need to wind the clock is an alternate rise 
and fall in air temperature, which is something that takes place without 
our interference. Could we call this clock a "perpetual motion" machine 




Weight 



Fig. 78. Diagram of another self-wind- 
ing clock 




Fig. 79. Self-winding clock. The pip 
with the glycerin is hidden in th 
base of the clock 



then? Of course not. The clock will tick indefinitely until its mechanism 
wears out, but what mak es it go is the heat of the surrounding air. The 
clock stores up the work of heat expansion and expends it portion 
after portion to turn its hands. This is really a "gift-power" machine 
since it does not require care or outlay. But it doesn't create energy out. 
of nothing; its primary source is the heat of the sun, which warms up the 
earth. 

Another specimen of a self-winding clock with a similar arrangement 
is given in Figs. 78 and 79. Its basic element is glycerin, which expands 
. when the temperature of the air rises and causes a small weight to rise. 
The lowering of this weight makes the clock go. Since glycerin solidi- 
fies only at 30 C below zero and boils at 290 C above, this mechanism 
is quite suitable for town clocks. A 2 temperature fluctuation is already 



114 



enough to keep it going. One such clock was tested for a whole year, 
and proved to be quite satisfactory. 

Can any advantage be derived by designing other bigger machines 
of this kind? At first glance, such a "gift-power" machine might seem 
very economical. Let us see, though, whether this is really so. To wind 
up an ordinary clock to run for 24 hours one requires only 1/7 kgm of 
energy. This is merely ^.IM of a kilogramme-metre per second. Con- 
sidering that one horsepower is equivalent to 75 kgm/sec, the power of 
one clock mechanism is equivalent to only 4 5i0 oo. ooo * a horsepower. 
Consequently, if the rods in the first clock mentioned or the contrap- 
tion of the second were to cost one kopek, the investment made to 
produce one h.p. would be 45,000,000 kopeks, or 450,000 rubles. I think 
half a million rubles for one horsepower is a bit too much for a "gift- 
power" machine. 

INSTRUCTIVE CIGARETTE 

Fig. SO shows a straw-tipped cigarette on top of a match box. Smoke 
is curling out of both ends. However, at one end it curls up, and at the 
other down. Why? After all, isn't the smoke coming out of the two ends 
the same? It is, of course, but above the smouldering end there is an 
ascending current of warm air which carries the particles of smoke up. 
Meanwhile the air carrying the smoke through the straw tip cools off 
and no longer rises upward; since the particles of smoke are heavier 
than air, they float down. 

ICE THAT DOESN'T MELT IN BOILING WATER 

Take a test tube, fill it with 
water, and put a lump of ice 
in. To keep the ice down at 
the bottom since it is light- 
er than water, it floats- press 
it down by some small weight, 
seeing to it that the water can 
get at the lump of ice. Now 

heat the test tube on a spirit _. _. _ 17l _ , , 

i *u * *u a i- i fl 8* W- Wh y does the smoke curl up from 

lamp so tnat tne flame licks one end, and down from the other? 





only at the tube's upper part as shown 
in Fig. 81. The water will soon boil 
o and send out steam. Oddly enough, 
J the ice at the bottom of the tube 
doesn't melt. A minor miracle, one 
ould think ice that doesn't melt 
in boiling water! 

The trick is that at the bottom of 
the tube the water doesn't boil at all; 
it remains cold. Actually we have not 
"ice in boiling water" but "ice be- 
neath boiling water". As it expands 



doesn't melt C r; it does not descend to the bottom 

and stays in the upper part of the 

tube. There is warm water and a mixture of warm and cold 
layers of water only in the tube's upper part. Heat can be transferred 
down only by a conductor, but water is a very poor conductor of heat. 



ON TOP OR BENEATH? 

When we want to heat water, we put the vessel that contains it right 
above the flame and not to the side of it. This is the right thing to do since 
the heated air which grows lighter is forced out from beneath the vessel 
upwards and thus envelops the vessel. So by placing the object we want 
to heat up right above the flame we use the source of heat in the most 
advantageous way. 

But what should we do to cool something with ice? Many put the 
thing they want to cool a jug of milk, for example on top of the ice. 
This is the wrong thing to do; as the air above the ice cools it descends, 
its place being taken by the warmer surrounding air. So if you want 
to cool a drink or a dish, don't put it on top of the ice but rather the 
ice on top of it. 

Let me make the point clearer. When we put a jar of water on top of 
ice, it is only the bottom layer that cools. The rest of the water is 
surrounded by uncooled air. But if wo put the ice on the lid, the water 



116 



will cool much faster. The cooled upper layers will descend, their place 
being taken by the warm layers rising from the bottom; the process 
goes on until all the water has cooled (note that pure water will cool 
not to zero but only to 4C above the temperature at which it possesses 
the greatest density. After all we never really cool drinks down to zero). 
Meanwhile the cooled air around the ice will also descend and envelop 
the vessel. 



DRAUGHT FROM CLOSED WINDOW 

We often feel a draught coming from a window that is closed tight 
and hasn't a single crack in it. Though it seems odd there is nothing at 
all surprising in it. 

The air inside a room is practically never in a state of rest. An 
invisible current circulates as the air warms or cools. As the air 
warms it rarefies and grows lighter. As it cools it becomes denser and 
heavier. 

The cold heavy air near the windows and outer wall descends to the 
floor, forcing the warm light air to rise to the ceiling. A toy balloon 
reveals this circulation at once. Tie a small weight to it, light enough 
to keep it suspended in mid-air. Release the balloon near the stove 
or radiator. You will see it travel around the room, being carried by 
the invisible current from the fireplace or radiator up to the ceiling and 
towards the window, and from there down to the floor and back to the 
fireplace. Here it again sets out on the same journey. That is why we 
feel the draught, especially around the feet, coming from the window 
though it is closed tight in winter. 



MYSTERIOUS TWIRL 

Take some thin cigarette paper and cut out a piece in the form of 
a rectangle. Fold it down the middle and then straighten it again. The 
fold will tell you where the centre of gravity is. Now stick a needle 
upright into the table and place the piece on the other end so that it 
is set on its centre of gravity and , hence, balanced . So far there is nothing 

117 




Fig. 82. Why does this piece of 
paper spin? 



mysterious about it. Bring up your 
hand as is shown on Fig. 82. Do this 
gently though, otherwise the piece of 
paper will be blown off by the rush 
of air. The paper will start to spin. 
At first it gyrates slowly but then it 
picks up speed. Take your hand away 
and gyration stops. Bring your hand 
up again and gyration resumes. 

This mysterious gyration once 
in the \ 870 's caused many to be- 
lieve that wo, or rather our bodies, were endowed with some super- 
natural properties. Mystics thought this confirmed their wild theories 
about the strange fluids the human body was supposed to possess. Ac- 
tually, there is nothing unnatural in it; as a matter of fact, everything is 
as simple as pie. When you bring your hand up, the air near it, which 
is warmed by its proximity, rises and, pressing against the piece of 
paper, causes it lo spin. It revolves because it is slightly folded, thus 
acting the same role as a curled piece of paper suspended above a 
lamp. 

A closer look will show you that the piece of paper always gyrates 
in one and the same direction from the wrist towards the finger-tips. 
This is because the finger-tips are always colder than the palm of the 
hand; consequently, the palm gives rise to a stronger ascending air 
current than the finger-tips. Incidentally, when one is feverish, or 
happens to be running a high temperature, the paper gyrates much 
faster. You might be interested to learn that this twirling, which once 
mystified so many, was the subject of a communication made to the 
Moscow Medical Society in 1876 (The Gyration of Liqht Bodies Caused 
by the Heat of the Hand, by N. P. Nechayev). 



DOES A WINTER COAT WARM YOU? 

If I told you that your fur coat does not warm you at all, you would 
probably think I was pulling your leg. But suppose I prove it? Stage 
the following experiment. Take the reading of an ordinary thermometer. 



118 



TJicn wrap it in your fur coat and let it be for some hours. Then read the 
thermometer again. It will be exactly the same as before. Has that 
convinced you that your fur coat doesn't warm you? Perhaps, it cools 
you then? Take two bags of ice and wrap one in your fur coat, leaving 
the other in a dish. When this second bag of ice melt s, unwrap the coat. 
The ice in the first bag has hardly melted at all. As you see, the coat 
has not warmed it in the least; on the contrary, it seems even to have 
cooled it, since the ice took longer to melt! 

So, does a winter coat warm you? No, if by warming we mean the 
communication of heat. A lamp does. So does a stove. And so does our 
body. They are all sources of heat. Your fur coat is not a source of heat; 
it doesn't have any warmth of its own to give. It merely prevents our 
body from shedding its own warmth. That is why a warm-blooded animal 
whose body is actually a source of heat feels much warmer in a coat 
of fur than without one. However, since the thermometer we took for 
our experiment is not a source of heat its reading naturally could not 
change simply because we wrapped it in the fur coat. The ice in the 
coat also took longer to melt because the coat is a rather poor conductor 
of heat and blocks any intake of surrounding warmth. 

The snow on the ground is also like a fur coat; it is a poor conductor 
of heatlike all powdery bodiesand thus prevents the ground beneath 
from shedding its heat. The temperature of the ground beneath a protec- 
tive layer of snow is often some 10 C higher than at a bare spot. 

So the answer to the question "Does a winter coat warm you? " is: 
it merely helps us to warm ourselves; rather we ourselves warm the 
coat instead . 

THE SEASON UNDERFOOT 

It is summer on the ground and above it. What season of the year 
is it three metres down? You think it's summer? You're wrongl It's not 
at all the same season as one might think. The point is that the ground 
is a very poor conductor of heat. In Leningrad water mains don't burst 
even in the grimmest of frosts, because they are two metres deep. Above- 
surface temperature fluctuations reach the different subsoil strata wilt 
great delay. Direct measurements conducted in the town of Slutsk, Lenin- 
grad Region, showed that at three metres down the warmest time of the 

119 



year comes 76 days late, while the coldest period is 108 days late. 
If the hottest day above the ground is July 25th, at three metres 
down the hottest day will come only on October 9th. On the other 
hand, if the coldest day is January 15th, at the depth given the 
coldest day will come only in May. At greater depths the delay is 
still greater. 

The further down we go, the weaker the temperature fluctuations 
become, to fade to an everlasting constant at a certain depth; here you 
have one and the same temperature round the year for centuries on end . 
This temperature is the mean annual temperature of the place in ques- 
tion. In the cellars of the Paris observatory, 28 metres below the ground, 
there is a thermometer which Lavoisier stored away there more than 
150 years ago. The mercury has not budged a hair since, giving all the 
time one and the same temperature of 11.7G above zero. 

To sum up: underfoot we never have the season of the year we have 
above the ground. When it is winter for us it is still autumn three metres 
down of course not the autumn we had, as the fall in temperature is 
not so pronounced. On the other hand, when it is summer for us, deep 
down we still have faint repercussions of winter frosts. One must always 
bear this important point in mind whenever one is dealing with the 
conditions of life underground for plant tubers and roots, and for 
cockchafer grub, for instance. It should not be surprising, for instance, 
that in tree roots the cells multiply in winter and that the tissue called 
the cambium ceases to function for practically the whole of summer, 
in contrast to the tissue of the above-ground tree-trunk. 



PAPER POT 

Look at Fig. 83. An egg is boiling in water in a paper cup. Won't the 
paper burn through and the water spill out and extinguish the flame? 
Try to do it yourself, boiling the egg in some stiff parchment paper 
attached fast to a piece of wire (or better make the paper box shown 
in Fig. 84). Nothing happens to the paper! The reason is that one can 
warm water only up to boiling point 100C. The water it has a 
great capacity for absorbing heat absorbs the paper's extra heat 
and prevents it from warming to much more than 100 C, that is, to 

120 




a point where it could burst 
into flame. The paper won't burn 
even if licked by the flame. 

It is the same property of wa- 
ter that prevents a kettle from 




Fig. 83. An egg boiling in a paper pot Fig. 84. A paper box for boiling water 

going to pieces which is what would happen wore we absent-minded 
enough to put the kettle on to boil without any water in it. For the same 
reason you must not put soldered pots on the fire unless they have 
water in them. The water used to cool the old Maxim machine guns 
saved the barrel from melting. 

By using a little box made from a playing card , you can melt a lead 
pellet. To do this, put the lead in the box right above the flame. Since 
lead is a good conductor of heat it rapidly absorbs the heat of the box, 
preventing the box from heating up to way above its molting point 
335 G which is too little yet for the box to break into flame. 

Fig. 85 gives another simple experiment. Take a thick nail or an 
iron or better copper rod and tightly curl screw-wise a narrow strip 





Fig. 85. Paper that doesn't 
burn 



Fig. 86. The thread that doesn't 
burn 



of paper around it. Then apply a flame. The flame will lick at the paper 
and even smoke it; but it'll start burning only when the rod grows red- 
hot. Again the metal's good heat conductivity is the reason. A glass 
stick, for instance, wouldn't do at all for this experiment. Fig. 86 shows 
a similar experiment in which we have a "non-inflammable" piece 
of thread wound tightly round a key. 

WHY IS ICE SLIPPERY? 

One slips on a smoothly polished floor much more easily than on 
one that isn't polished. Now, shouldn't smooth ice be much more slip- 
pery than bumpy ice? However, contrary to expectation, a sled goes 
much more easily over bumpy ice than over smooth ice which you may 
have noticed yourself if you have ever happened to pull a sled. How 
come that bumpy ice is more slippery than glossy ice? Ice is slippery 
not because it's smooth but because its melting point drops when pres- 
sure is increased. 

Let's see what happens when we sled or skate. On skates we bring 
the whole weight of our body to bear down on a very small area, of 
but a few square millimetres. Recall Chapter 2 of this book. You will 
realise that a person on skates exerts a considerable pressure on the ice. 
Under strong pressure ice melts at a lower temperature. For instance, 
if the temperature of the ice is 5C below zero and the skater's pressure 
has lowered the melting point of the ice beneath his skates by 
6 or 7, this ice will melt. This gives rise to a thin layer of water 
between the blades and the ice. No wonder the skater slides, or rather 
slips, along/ And as soon as he moves further, the same thing repeats 
itself. The skater continually slides over a thin layer of water. It is only 
ice that has this property. One Soviet physicist even called it "nature's 
sole slippery body". All other bodies are smooth but not slippery. 

Back now to our first point. Why is bumpy ice more slippery than 
smooth ice? We already know that one and the same weight exerts a 
stronger pressure when it rests on a smaller area. When does a man 
exert more pressure? On smooth ice? Or on bumpy ice? It is quite ob~ 
vious that he exerts more pressure on bumpy ice because in this case he 
is supported ^nly by a few bumps in the ice. The greater the pressure 

122 



exerted, the more readily does ice melt and, consequently, the more 
slippery does ice become provided the sled runners are wide enough 
(this will not apply to the thin skate blades as the energy of motion 
is expended to slice off the bumps). 

This pressure- induced lowering of the melting point of ice explains 
many other things that we see around us. This is why separate lumps 
of ice freeze into one when strongly pressed together. Boys throwing 
snowballs unconsciously avail themselves of this property; the separate 
snowflakes stick together because the pressure exerted to form the snow- 
ball lowers their melting point. To make a snowman wo again apply 
this principle. (I suppose I needn't explain, though, why in strong frosts 
wo are unable to mould good snowballs and snowmen.) Under the pres- 
sure of the many feet walking along the pavement snow gradually turns 
into one solid icy mass. 

It has been theoretically calculated that to lower the melting point 
of ice by one degree Centigrade we must exert the rather considerable 
pressure of 130 kg/cm 2 . Hero one must bear in mind that in the process 
of melting both ice and water are subjected to one and the same pres- 
sure. In the instances described it was only the ice that was subjected 
to strong pressure; the water the ice melted into is subjected to at- 
mospheric pressure; consequently, in this case the effect pressure has 
on the melting point of ice is much greater. 

THE ICICLES PROBLEM 

Have you ever stopped to wonder how the icicles we see drooping 
from eaves form? And when do they form? During a thaw or during a 
frost? And if during a thaw, then how does water freeze at an above- 
zero temperature? On the other hand, if during a frost, then where, in 
general, does the water that freezes come from? 

As you see, the problem is not so simple as you may have thought. 
To produce icicles you need two temperatures simultaneouslyone 
above zero for melting and the other below zero for freezing. That is 
really what happens. The snow on slanting rooftops melts because it is 
warmed by the sun to an above-zero temperature. Meanwhile the drops 
of water dripping off the eaves freeze, because here we have a sub-zero 



*?3* 4^ / , ^Tissfe 




Fig. 87. The sun beats the slanted roof more than the ground 



temperature. (We don't mean the icicles that form because of the warmth 
exuded by the heated room under the roof.) 

Try to imagine the following picture. It's a clear and sunny day. 
The temperature is just one or two degrees Centigrade below zero. Every- 
thing is bathed in sunlight. The sun's slanting rays are not strong 
enough to melt the snow on the ground. But since they strike the in- 
clined rooftop facing the sun at an angle closer to a right angle, they 
warm up the roof and. melt the snow on it. Sunshine gives more light 
and warmth the wider the angle between the line of the rays and the 
plane on which they are incident. It acts in direct ratio to the sine of 
this angle. As for the case in Fig. 87, the snow on the rooftop gets 2.5 
times more warmth than the snow on the ground , because the sine of 60 is 
2.5 times more than the sine of 20. The melting snow drips off the eaves* 
But since the temperature beneath the eaves is a sub-zero one the drops 
of water cooled furthermore by evaporation freeze. Another drop 
drips onto the frozen one and also freezes. Then comes a third, a fourth 

124 



and so on, gradually producing a tiny pendant of ice. A couple of days 
later, or maybe a week later, we have the same kind of weather again. 
The pendant grows, producing a larger and larger icicle in much the 
same way as lime stalactites form in underground caverns. That is how 
icicles form on the eaves of sheds and other unheated premises. 

The changing angle of incidence of the sun's rays produces far grander 
phenomena. The different climatic zones and seasons are largely due 
to that but not wholly; another major factor is the varying day-length, 
or the time during which the sun warms the earth, which, like the sea- 
sons, is due to one and the same astronomical cause, the inclination 
of the earth's axis of rotation to the plane of the ecliptic. In winter the 
sun is practically as far away from us as in summer; it is just as far 
away from the poles as it is from the equator the difference is so 
insignificant that it can be totally ignored. However, at the equa- 
tor the angle of incidence of the sun's rays is wider than at the poles; in 
summer again, the angle of incidence is wider than in winter. This 
phenomenon gives rise to a pronounced variation in temperatures, and 
consequently in nature in general. 



CHAPTER SEVEN 

LIGHT 



TRAPPED SHADOWS 

Our forefathers did find some use for their shadows even though they 
weren't able to catch them. This was the making of silhouettes, or shadow 
images. Today we go to the photographer's if we want our pictures or 
the pictures of friends and relatives taken. But in the 18th century there 
were no photographers. Portrait-painters asked a stiff price for their 
work and only the rich could afford it. That is why silhouettes were so 
widespread; in some measure they did for our present snapshots. 

Silhouettes are actually trapped shadows. They were obtained mechani- 
cally and in this we can draw a certain parallel between them and their 
opposites photographs; while photographers draw on light ("photos" 
is Greek for light) to make pictures, our ancestors used shadows for the 
same purpose. 

Fig. 88 shows you how silhouettes were made. The sitter turned his 
head to cast a characteristic profile and this profile was traced with a 
pencil. Then the inside of the outline was blacked, cut out, and glued 
onto a white ground. This was the silhouette. Whenever necessary, the 
silhouette was reduced by means of a special device called the panto- 
graph (Fig. 89). 

Don't think that this simple black outline could not give a notion of 
the characteristic features and profile of its prototype. A good silhouette 
is sometimes amazingly like the original. 

This property intrigued some artists, who began to paint in this man- 
ner, thus starting a whole school. The very origin of the word is of 
interest. It derives from Etienne de Silhouette, an 18th-century 

126 




Fig. 88. An old way of making shadow portraits 





Fig. 89. How to reduce 
a silhouette 



Fig. 90. A silhouette 
of Schiller (1790) 



French Minister of Finance, who urged his extravagant compatriots to 
show thrift and reproached the French aristocracy for wasting money 
on pictures and portraits. The cheapness of shadow likeness thus sug- 
gested the nameportraits "i la Silhouette". 



THE CHICK IN THE EGG 

The properties shadows possess will enable you to stage an amusing 
parlour trick. Take a piece of greased paper and make a screen by stick- 
ing it on top of a square hole cut in a piece of cardboard. Put two 
unshaded table lamps behind this screen and seat your friends in front of 
it. Switch on the left lamp. Place an oval piece of cardboard mounted 
on a piece of wire between the lit lamp and the screen. Your friends 
will naturally see the outline of an egg. The second lamp is still not on. 
Now tell your friends that you have an X-ray machine that will detect 
the chick inside the egg. Hey, presto! and your friends sec the egg's 
shadow pale and the rather distinct outline of a chick appear in the 
middle (Fig. 91). 

It is really all very simple. Just switch on the right lamp 
which has a cardboard chick between it and the screen. Part of 
the oval shadow upon which the chick's shadow is superimposed is 

illumined by the right lamp. That is 
why its fringes are lighter. Since your 
friends don't see your manipulations, 
those ignorant of physics and anato- 
my may really think that you have 
X-rayed the egg. 



PHOTOGRAPHIC CARICATURES 

Many of you might not know that 
you can make a camera in which an 
ordinary small round hole will take 
the place of the lens. True, you get a 
fainter image in this case. An inter- 
esting modification of this "lensless" 




Fig. 91. A fake X-ray 



camera is the "slit" camera which has two criss-crossing slits 
instead of the round aperture. This camera has in its front part two 
small slats, one having a vertical slit and the other a horizontal slit. 
When the two slats are superimposed the image obtained is the same 
as produced by the aperture camera. In other words, the likeness is not 
distorted. But when the slats are moved apart they are specially ar- 
ranged so that this can be done the image produced becomes distorted 
(Figs. 92 and 93), resembling a caricature rather than a photograph. 





Fig. 92. A caricature obtained by 

moans of a "slit" camera. The 

image is distended horizontally 



Fig. 93. A similar cari- 
cature distended verti- 
cally 



Why does this happen? Let us take the case when the slat with the 
horizontal slit is placed in front of that with the vertical slit (Fig. 94). 
The rays coming from the vertical line of figure D (a cross) pass 
through the first slit C as through any ordinary aperture; meanwhile 
slit B does not alter their course at all. Consequently, on the ground- 
glass screen A you get an image of the vertical line on a scale corre- 
sponding to the distance between A and C. However, this disposition of 
the slats produces an entirely different image of D's horizontal line. 
The rays pass through the horizontal slit without hindrance and don't 
cross until they reach the vertical slit B, which they pass as any round 



92668 



129 



aperture to produce on screen A an image on a scale corresponding to 
the distance between A and B. 

In short, the vertical lines are taken care of by slit C only, and the 
horizontal lines, on the contrary, by slit B only. Since slit C is further 
away from the screen all vertical dimensions are reproduced on glass 
A on a scale larger than that of the horizontal dimensions. In other 




Fig. 94. Why the "slit" camera produces distorted images 

words the image is distended vertically. A redisposition of the slats 
will produce a horizontally distended likeness (compare Figs. 92 
and 93). A slantwise disposition will distort the likeness in still 
another way. 

This camera can be employed not only to get caricatures. It can also 
serve a more serious purpose, as, for instance, to vary architectural 
embellishments, carpet and wallpaper patterns, and in general any 
ornamental motif that may be distended or condensed at will in a 
definite direction. 

THE SUNRISE PROBLEM 

Suppose you get up exactly at 5 o'clock early in the morning to watch 
the sunrise. Since light does not propagate instantaneously some time 
must pass before the light reaches your eye from its source. So my ques- 
tion is: At what time would you see the sunrise were light able to 
propagate instantaneously? 

Since it takes eight minutes for the light to travel from the sun to us 
here on Earth, one might think that if light propagated instantaneously 

130 



one would see the sun rise eight minutes earlier at 4:52 a.m. You're 
in for a surprise if you think so; that answer is absolutely wrong. The 
sun "rises" when the Earth turns to face the space that is already lit. 
Therefore even if light propagated instantaneously we would still see 
the sunrise only at 5 a.m. 

If we take what is called " atmospheric refraction " into consideration 
we get a still more startling result.' Refraction curves the path of light, 
thus enabling us to see the sun "rise" before it really rises above the 
horizon. But if light propagated instantaneously, there would be no 
refraction as this is due to the different velocities with which light 
travels in different media. And as there would be no refraction, we would 
see the sun rise a bit later from two minutes to as much as several 
days and even more (in polar latitudes), as this would depend on the 
latitude, air temperature, and certain other factors. So, were light to 
propagate] instantaneously we would see tho sunrise later than wo do 
now. A most curious paradox! (See Do You Know Your Physics? for 
further detail.) 

It would be quite different, of course, if you were observing the ap- 
pearance of a solar protuberance in a telescope. Then that is, if light 
propagated instantaneously you would see it eight minutes earlier. 



9* 



CHAPTER BIGHT 

REFLECTION AND REFRACTION 

SEEING THROUGH WALLS 

In the 1890's one could buy a curious contraption pompously called 
an "X-ray apparatus". I remember how puzzled I was when I, a school- 
boy at the time, saw this ingenious device for the first time. It enabled 
me to see light through opaque objects not only thick paper but even 
a knife blade, which is impenetrable to real X-rays. Fig. 95, which 
shows the prototype of the contraption I just mentioned, "lets the cat 
out of the bag ". It has four small mirrors , each slanted at the angle of 
45, to reflect and rere fleet the rays coming from the object and thus 
lead them around the opaque obstacle. 




Fig. 95. A sham X-ray apparatus 



The military extensively employ a similar device the periscope 
{Fig. 96) enabling them to follow the enemy's movements without ex- 
posing themselves to the hazard of enemy fire. The further away the 




Fig. 96. The periscope 



Fig. 97. Diagram qf a subma- 
rine periscope 



object is from the periscope, the smaller the observer's field of vision 
is. A special arrangement of optical lenses is used to enlarge the field 
of vision. But since the lenses absorb part of the light that enters the 
periscope, the image* obtained is blurred. This limitsi the height of a 

133 



periscope, with some twenty metres being already close to the "ceiling ". 
Taller periscopes give a very small field of vision and a blurred image, 
especially in cloudy weather. 

Submarine commanders also use periscopes to watch the ships they 
attack. Though a far more complicated affair than the army periscope, 
this periscope, which juts out of the water when the submarine sub- 
merges, is the same in principle, having a similar arrangement of 
mirrors (or prisms). (Fig. 97.) 

THE SPEAKING HEAD 

This frequent side-show "marvel" dumbfounds the uninitiated. It 
does, indeed, astound one to see on a plate a live, seemingly severed 
human head, which rolls its eyes, speaks, and eats. And though you can't 
walk right up to the table on which it lies, you "quite perfectly" see 
that there is nothing underneath. If you ever see this side show, make a 
paper ball and throw it under the table. Strangely enough, it bounces 
back. The mystery is no longer a mystery it has bounced off a mirror. 
Even if it doesn't reach the table it will show you that there is a mirror 
there because you will see its reflection (Fig. 98). 

It is quite enough to have a mirror stretching from one table-leg to 
the other to give one the illusion that there is nothing beneath the 
table provided, of course, that the mirror doesn't reflect the furnishings 
of the room or the audience. That is why it is absolutely necessary for 
the room to be bare and its walls all alike. The floor too should be in one 

tone, devoid of all ornamental design, and 
the audience must be kept at a respectful 
distance. As you see, the "secret" is as 
simple as pie, but until you're in the know, 
you just gape. 

Sometimes the trick is still fancier. First 
the conjuror shows you a bare table, with 
nothing on top or beneath it. Then a closed 
box that is supposed to have the "live 
head " inside, but which is really empty, 

is bt0 ODt ** St ' T1e COn J Ur r 




Fig. 98. The secret of the 

lopped-off head puts the box on the table and opens up 



the front flap. And lo! a speaking head appears. You've most 
likely guessed that the upper board of the table has sort of a trap-door 
in it through which the man squatting under the table behind the 
mirror pokes his head when the bottomless empty box is placed on the 
table. There are other ways of doing this trick. You'll probably be 
able to work it out for yourself. 

IN FRONT OR BEHIND 

There are many household things which are not used properly. You 
already know that some don't use ice properly to cool a drink; they place 
it on top of the ice instead of beneath the ice. Nor does everyone know 
how to use a mirror properly. Quite often one may put a lamp behind 
oneself to "light up" one's reflection in the mirror instead of throwing 
the light on one's own person. Since there are many women who do 
that, I hope the women among my readers will put the lamp in front of 
themselves when they want to use a mirror. 

IS A MIRROR VISIBLE? 

There, again, is proof that what we know about the ordinary mirror is 
not enough, because most answer this question wrongly, even though 
all use mirrors every day. Those who think that they can see a mirror 
are mistaken. A good, clean mirror is invisible. You can see its frame, 
its rim and everything reflected in it, but you'll never see the mirror 
itself unless it's dirty. In contrast to a dispersing surface one that 
scatters light in all directions every reflecting surface is invisible. In 
ordinary practices a reflecting surface is a polished one, and a dispers- 
ing surface, a dull one. All tricks and optical illusions using mirrors- 
the "speaking head ", for instance are based precisely on their invisi- 
bility. All that you do see is the reflection in the mirror of different 
objects. 

IN THE LOOKING-GLASS 

When we look in the looking-glass we see ourselves, many will say, 
adding that what we see is the exact copy of our own person down 
to the minutest detail. 

135 



Let's 'test that statement. Suppose you have a mole on your right 
cheek. The person you see in the mirror has a mole on his left cheek. You 
may be brushing your hair to the right; your double in the mirror will be 
doing it to the left. Your right brow may be a bit higher and thicker 
than your left one; with your copy in the mirror it's the other way 
round. You keep your watch in your right waistcoat pocket and your 
wallet in the left pocket; your double has quite opposite habits. Note the 

dial of his watch. Your watch isn't at all like 
that. The figures and their arrangement are 
most unusual. You see an eight marked as it 
has never been marked before as I1X and 
standing where the twelve ought to be. 
Meanwhile there is no twelve at all. After a 
six comes a five, a four and so on. The hands 
of the watch's double in the mirror move the 
other way. 

To cap it all, he has a physical handicap 
which you most likely don't have. He's left- 
handed. Ho writes, sews and eats with his 
left hand. And he'll stretch out his left hand 

to shake your right one. Then, does he know his letters? At any rate 
his knowledge is of a most peculiar brand. I greatly doubt whether 
you will ever be able to read a single line in the book he holds or 
make out a single word in his left-handed scribble. Such is the person 
who claims to be your exact copy, the person you claim is exactly 
like you! 

But joking apart, if you really think that by looking in the mirror you 
are observing yourself, you are mistaken. The face, body and clothing 
of most people are not strictly symmetrical, but usually we don't notice 
that. The right side is not quite the same as the left side. In the 
looking-glass your left side assumes all the peculiar features of 
your right side and vice versa, so that you actually have a reflec- 
tion that often produces quite a different impression than you do 
yourself. 




Fig. 99. Use a mirror 



136 



MIRROR DRAWING 

The fact that you and your reflection are not totally alike stands out 
still more when you do the following. Sit down at a table facing an 
upright mirror. Then take a piece of paper and try to draw, say, a rec- 
tangle with intersecting diagonals, by looking at the reflection of your 
hand. This seemingly simple task becomes incredibly difficult. 




Fig. 100. Drawing in front of a looking-glass 

As we grow up our visual impressions and motive sensations reach a 
definite degree of accord. The mirror violates this harmony as it gives 
us a distorted visual image of our hands in motion. Force of habit cries 
out against every move you make: you want to draw a line towards the 
right, but your hand pulls the pencil towards the left. You get still 
stranger results when you try in this manner to draw still more intri- 
cate figures or write something. You are bound to make a jnost comical 
mess of things. 

The inky imprints on blotting paper are also a mirror-like symmetri- 
cal reflection of your handwriting. But try to read them. You won't 
be able to make out a single word, even when the letters seem quite 

137 



distinct. The writing will be slanted left wise and all the strokes are 
topsy-turvy. However, as soon as you try to read this muddle in a mir- 
ror, everything straightens itself out and you recognise your own cus- 
tomary handwriting. Actually, the mirror gives you a symmetrical 
reflection of what in itself is a symmetrical reflection of your own hand- 
writing. 

SHORTEST AND FASTEST 

In a homogeneous medium light propagates rectilinearly, that is in 
the fastest way possible. Light again picks the fastest route when reflect- 
ing from a mirror. Let us trace its passage. In Fig. 101 A is the source 





Fig. 101. The angle of reflection 2 
is equal to the angle of incidence 1 



Fig. 102. Reflecting light chooses 
the shortest path 



of light, a candle, MN a mirror, and ABC the ray's passage from 
A to the eye C. The straight line KB is perpendicular to MN. 

According to the laws of optics, the angle of reflection 2 is equal to 
the angle of incidence 1. Once we know this, we can easily prove that of 
all possible routes from A to C, that bounce off the mirror MN, ABC is 
the shortest. To prove that .this is so, let us compare ABC with some oth- 
er route for example, ADC (Fig. 102). Drop the perpendicular AE from 
point A onto MN and continue it further until it intersects with the 
continuation of the ray BC at point F. Then join points F and D by a 



138 



straight line. Now let us see first whether the two triangles ABE and 
EBF are equal. They are both right triangles and both have the side EB 
adjacent to the right angle. Besides that, the angles EFB and EAB are 
equal as they are respectively equal to the angles 2 and 1. Consequent- 
ly, AE is equal to EF. Hence, the right triangles AED and EDF are 
equal because their respective sides adjacent to the right angles are 
equal. Consequently, AD is equal to DP. 

We can thus replace the route ABC by the equal CBF route since 
AB is equal to FB and the ADC route by the CDF route. Comparing 
CBF and CDF, we see that the straight line CBF is shorter than the 
broken line CDF. Consequently, the ABC route is shorter than the 
ADC one. Q.E.D.! 

Wherever point D may be, the ABC route will always be shorter 
than the ADC one, provided of course the angle of reflection is equal 
to the angle of incidence. As we see, light indeed chooses the shortest 
and fastest of all possible routes between its source, the mirror, and the 
eye. This was first pointed out by Hero of Alexandria, that celebrat- 
ed 3rd-century Greek mathematician. 

AS THE CROW FLIES 

The ability to find the shortest way in cases like the one we dis- 
cussed may come in handy when solving some brain-teasers. Take the fol- 
lowing case. 




Fig. 103. The problem of the crow. 
Find the shortest line of flight 
to the ground and to the fence 




Fig. 104. The solution of the 
problem of the crow 



A crow is perched on a branch, and there are some grains of millet 
scattered on the ground below. The crow swoops down, pecks at the mil- 
let and then flies up to perch on the fence. The question is: Where should 
.the crow peck in order to take the shortest possible route? (Fig. 103.) 
This is an absolutely similar problem to the one just discussed. So we 
can easily supply the right answer: the crow should follow the path 
of the ray of light. In other words, it should fly so that angle 1 is equal 
to angle 2 (Fig. 104), which, as we already know, is the shortest way 
possible. 

THE KALEIDOSCOPE 

I suppose you all know what the kalei- 
doscope is. This amusing toy has a handful 
of various coloured bits of glass which am 
placed between two or three flat mirrors. 
They form extremely beautiful figures which 
change symmetrically with the slightest 
twist of the kaleidoscope. Though a very 
common toy, few suspect the tremendous 
assortment of different patterns r one can 
get. Imagine that you have a kaleidoscope 
with 20 bits of glass inside and turn it 
to get ten new patterns every minute. How 
much time would you need to see all the 
patterns these 20 bits of glass could form? 
Even the wildest of imaginations would nev- 
er provide the right answer. The oceans would dry and the mountains 
crumble before you saw all; you would need at least 500,000 million 
years to see every figure produced! 

The infinitely different and eternally changing patterns that this toy 
provides have long intrigued art designers, whose combined imagina- 
tions-will never match the inexhaustible ingenuity with which it sug- 
gests loVely ornamental motifs for wallpaper, carpets and other fabrics. 
But among the general public it no longer excites the interest it did 
a hundred years ago when it was a fascinating novelty and when poets 
composed odes in its honour. ... > ' 



Fig. 105. A kaleidoscope 



140 



The kaleidoscope was invented in England in 1816. Some twelve to 
eighteen months later it was already arousing universal admiration. 
In the July 1818 issue of the Russian magazine Blagonamerenni (Loyal), 
the fabulist A. Izmailov wrote about it: "Neither poetry nor prose 
can describe all that the kaleidoscope shows you. The figures change 
with every twist, with no new one alike. What beautiful patterns! 
How wonderful for embroidering! But where would one find such bright 
silks? Certainly a most pleasant relief from idle boredom much better 
than to play patience at cards. 

"They say that the kaleidoscope was known way back in the 17th 
century. At any rate, some time ago it was revived and perfected in 
England to cross the Channel a couple of months ago. One rich French- 
man ordered a kaleidoscope for 20,000 francs, with pearls and gems in- 
stead of coloured bits of glass and beads. " 

Izmailov then provides an amusing anecdote about the kaleidoscope 
and finally concludes on a melancholic note, extremely characteristic 
of that backward time of serfdom: "The imperial mechanic Rospini, 
who is famed for his excellent optical instruments, makes kaleidoscopes 
which he sells for 20 rubles a piece. Doubtlessly, far more people 
will want them than to attend the lectures on physics and chemistry from 
which to our regret and surprise that loyal gentleman, Mr. Rospini, 
has derived no profit. " 

For long the kaleidoscope was nothing more than an amusing toy. 
Today it is used in pattern designing. A device has been invented to 
photograph the kaleidoscope figures and thus mechanically provide 
sundry ornamental patterns. 

PALACES OF ILLUSIONSJAND; MIRAGES 

I wonder what sort of a sensation we would experience if we became 
midgets the size of the bits of glass and slipped into the kaleidoscope? 
Those who visited the Paris World Fair in 1900 had this wonderful 
opportunity. The so-called "Palace of Illusions " was a major attraction 
there a place very much like the insides of a huge rigid kaleidoscope. 
Imagine a hexagonal hall, in which each of the six walls was a large, beau- 
tifully polished mirror. In each corner it had architectural embellish- 

141 



ments columns and cornices which merged with the sculptural 
adornments of the ceiling. The visitor thought he was one of a teeming 
crowd of people, looking all alike, and filling an endless enfilade of 
columned halls that stretched on every side as far as the eye could 
see. The halls shaded horizontally in Fig. 106 are the result of a single 
reflection, the next twelve, shaded perpendicularly, the result of a 
double reflection, and the next eighteen, shaded slantwise, the result 
of a triple reflection. The halls multiply in number with each new mul- 




Fig. 106. A three-fold reflection from the walls of the central 
hall produces 36 halls 



tiple reflection, depending, naturally, on how perfect the mirrors are 
and whether they are disposed at exact parallels. Actually, one could 
see only 468 hallsthe result of the 12th reflection. 

Everybody familiar with the laws that govern the reflection of light 
will realise how the illusion is produced. Since we have here three pairs 
of parallel mirrors and ten pairs of mirrors set at angles to each other, no 
wonder they give so many reflections. 

The optical illusions produced by 
the so-called Palace of Mirages at 
the same Paris Exposition were still 
more curious. Here the endless 
reflections were coupled with a 
quick change in decorations. In 
other words, it was a huge but 
seemingly movable kaleidoscope, 
with the spectators inside. This 
was achieved by introducing in the 
hall of mirrors hinged revolving 
corners much in the manner of a 
revolving stage. Fig. 107 shows 
that three changes, corresponding 
to the corners 7, 2 and 5, can be 
effected. Supposing that the first six 
corners are decorated as a tropical 





Fig. 107 



Fig. 108. The secret of 
the "Palace of Mirages" 



forest, the next six corners as the interior of a sheikh's palace, 
and the last six as an Indian temple. One turn of the concealed mecha- 
nism would be enough to change a tropical forest into a temple or 
palace. The entire trick is based on such a simple physical phenome- 
non as light reflection. 

WHY LIGHT REFRACTS AND HOW 

Many think the fact that light refracts when passing from medium to 
medium is one of Nature's whims. They simply can't understand why 




Fig. 109. Refraction of light explained 

light does not keep on in the same direction as before but has to strike 
out obliquely. Do you think so too? Then you'll probably be delighted 
to learn that light behaves just as a marching column of soldiers does when 
they step from a paved road to one full of ruts. 

Here is a very simple and instructive illustration to show how light 
refracts. Fold your tablecloth and lay it on the table as shown in Fig. 
109. Incline the table-top slightly. Then set a couple of wheels on one 
axle from a broken toy steam engine or some other toy rolling down 
it. When its path is set at right angles to the tablecloth fold there is 
no refraction, illustrating the optical law, according to which light fall- 
ing perpendicularly on the boundary between two different media does 
not bend. But when its path is set obliquely to the tablecloth fold the 
direction changes at this point the boundary between two different 
media, in which we have a change in velocity. 

144 



When passing from that part of the table where velocity is greater 
(the uncovered part) to that part where velocity is less (the covered 
part), the direction ( "the ray ") is nearer to the "normal incidence ". When 
rolling the other way the direction is farther away from the normal. 

This, incidentally, explains the substance of refraction as due to the 
change in light velocity in the new medium. The greater this change is, 
the wider the angle ol refraction is, since the "refractive index", which 
shows how greatly the direction changes, is nothing but the ratio of the 
two velocities. If the refractive index in passing from air to water is 
4/3, it means that light travels through the air roughly 1.3 times faster 
than through water. This leads us to another instructive aspect of light 
propagation. Whereas, when reflecting, light follows the shortest route, 
when refracting, it chooses the fastest way; no other route will bring 
it to its "destination' 1 sooner than this crooked road. 

LONGER WAY FASTER 

Can a crooked route really bring us sooner to our destination than the 
straight one? Yes when we move with different speeds along different 
sections of our route. Villagers living between two railway stations A 
and B 9 but closer to A, prefer to walk or cycle to station A and board 
the train there for station J?, if they want to get to station B faster, 
than to take the shorter way which is straight to station /?. 

Another instance. A cavalry messenger is sent with despatches from 
point A to the command post at point 
C (Fig. 110). Between him and the 
command post lie a strip of turf and a 



T f 



strip of soft sand, divided by the 
straight line EF. We know that 
it takes twice the time to cross 
sand than it does to cross turf. Which 
route would the messenger choose sand 

to deliver the despatches sooner? 
At first glance one might think it 

to be the straight line between A F }8- no - The problem of the cav- 
, ~ TJ . T j u *u- i i alr y messenger. Find the fastest 

and C. But I don t think a single way from A to C 

102668 



horseman would pick that route. After all, since it takes a longer time 
to cross sand, a cavalryman would rightly think it better to cut the time 
spent by crossing the sand less obliquely. This would naturally length- 
en his way across the turf. But since the horse would take him 
across it twice as fast, this longer distance would actually mean less 
time spent. In other words, the horseman should follow a road that 
would refract on the boundary between sand and turf, moreover, with 
the path across the turf forming a wider angle with the perpendicular 
to this boundary than the path across the sand. 



Turf 



Sand 




Fig. 111. The problem of the cavalry 
messenger and its solution. The fast- 
est way is AMC 



Fig. 112. What is the sine? The rela- 
tion of rn to the radius is the sine 
of angle 7, while the relation of n 
to the radius is the sine of angle 2 



Anyone will realise that the straight path AC is actually not the quick- 
est way and that considering the different width of the two strips and 
the distances as given in Fig. 110, the messenger will reach his destina- 
tion sooner if he takes the crooked road AEC (Fig. 111). Fig. 110 gives 
us a strip of sand two kilometres wide, and a strip of turf three kilome- 
tres wide. The distance BC is seven kilometres. According to Pythagoras, 



the entire route from A to C (Fig. Ill) is equal to J/ 5 2 + 7 2 
=8.6 km. Section .47V across the sand is two- fifths of this, or3.44 km. 
Since it takes twice as long to cross sand than it does to cross turf, the 
3.44 km of sand mean from the time angle 6.88 km of turf. Hence the 
8.6 km straight-line route AC is equivalent to 12.04 km across turf. Let 
us now reduce to "turf" the crooked AEC route. Section AE is two kilo- 



146 



metres, which corresponds to four kilometres in time across turf. Sec- 
tion EC is equal to |/3 2 + 7 2 =J/1>8 =7.6 km, which, added to 
four kilometres, results in a total of 11.6 km for' the crooked AEC 
route. 

As you see, the "short" straight road is 12 km across turf, while the 
"long" crooked road only 11.6 km across turf, wmcn thus saves 12.00 
11.60=0.40 km, or nearly half a kilometre. But this is still not the 
quickest way. This, according to theory, is that we snail have to invoke 
trigonometry in which the ratio of the sine of angle b to the sine of 
angle a is the same as the ratio of the velocity across turf to that across 
sand, i. e., a ratio of 2:1. In other words, we must pick a direction along 
which the sine of angle b would be twice the sine of angle a. Accord- 

ingly, we must cross the boundary bet ween the sand and turf at point M, 

f* 
which is one kilometre away from point E. Then sine b = ./ &*& , while 

1 sin 66161 

sme a ^" ' and the ratio of 



which is exactly the ratio of the two velocities. What would this route, 



reduced to "turf", be? AM = V 2 2 + ! 2 -4.47 km across turf. 

= V /r 3 a + 6 r 6.49 km. This adds up to 10.96 krn, which is 1.08 km 

shorter than the straight road of 12.04 km across turl. 

This instance illustrates the advantage to be derived in such circum- 
stances by choosing a crooked road. Light naturally takes this fastest 
route because the law of light refraction strictly conforms to the proper 
mathematical solution. The ratio of the sine oi the angle of refraction 
to the sine of the angle of incidence is the same as the ratio of the veloc- 
ity of light propagation in Uie new medium to that in the old medium; 
this ratio is the refractive index for the speciiied media. Wedding tht> 
specific features of reflection and refraction we arrive at the "Format 
principle" or the "principle of least time" as physicists sometimes 
call it according to which light always takes the fastest route. 

When the medium is heterogeneous and its refractive properties change 
gradually as in our atmosphere, for instance again "the principle 
of least time" holds. This explains the slight curvature in light as it 
comes from the celestial objects through our atmosphere. Astronom- 

10* 147 



era call this "atmospheric refraction". In our atmosphere, which be- 
comes denser and denser the closer we get to the ground, light bends in 
such a way that the inside of the bend faces the earth. It spends more 
time in higher atmospheric layers, where there is less to retard its 
progress, and less time in the "slower " lower layers, thus reaching its 
destination more quickly than were it to keep to a strictly rectilinear 
course. 

The Format principle applies not only to light. Sound and all waves in 
general, whatever their nature, travel in accord with this principle. 
Since you probably want to know why, lot me quote from a paper which 
the eminent physicist Schrodingor read in 1933 in Stockholm when re- 
ceiving the Nobel Prize. Speaking of how light travels through a medi- 
um with a gradually changing density, he said: 

"Let the soldiers each firmly grasp one long stick to keep strict breast- 
line formation. Then the command rings out: Double! Quick! If the 
ground gradually changes, first the right end, and then the left end will 
move faster, and the breast-line will swing round. Note that the route 
covered is not straight but crooked. That it strictly conforms to the 
shortest, as far as the time of arrival at the destination over this partic- 
ular ground is concerned, is quite clear, as each soldier tried to run as 
fast as he could . " 

THE NEW CRDSOES 

If you have read Jules Verne's Mysterious Island, you might re- 
member how its heroes, when stranded on a desert isle, lit a fire though 
they had no matches and no flint, steel and tinder. It was lightning that 
helped Defoe's Robinson Crusoe; by pure accident it struck a tree and set 
fire to it. But in Jules Verne's novel it was the resourcefulness of an edu- 
cated engineer and his knowledge of physics that stood the heroes in 
good stead. Do you remember how amazed that naive sailor Pencroft 
was when, coming back from a hunting trip, he found the engineer and 
the reporter seated before a blazing bonfire? 

"'But who lighted it? 1 asked Pencroft. 

"'The sun!' 

"Gideon Spilett was quite right in his reply. It was the sun that had 

148 



furnished the heat which so astonished Pencroft. The sailor could scarce 
ly believe his eyes, and he was so amazed that he did not think of 
questioning the engineer. 

"'Had you a burning-glass, sir? 1 asked Herbert of Harding, 

"'No, my boy/ replied he, 'but I made one.' 

"And he showed the apparatus which served for a burning-glass. It 
was simply two glasses which he had taken off his own and the reporter's 
watch. Having filled them with water and rendered their edges adhesive 
by means of a little clay, he thus fabricated a regular burning-glass, 
which, concentrating the solar rays on some very dry moss, soon 
caused it to blaze." 

I dare say you would like to know why the space between the two 
watch glasses had to be filled with water. After all, wouldn't an air- 
filling focus the sun's rays well enough? Not at all. A watch glass is 
bounded by two outer and inner parallel (concentric) surfaces. 
Physics tells us that when light passes through a medium bounded by 
such surfaces it hardly changes its direction at all. Nor does it bend 
when passing through the second watch glass. Consequently, the rays 
of light cannot be focussod on ono point. To do this we must fill up the 
empty space between the glasses with a transparent substance that would 
refract rays better than air does. And that is what Jules Verne's engi- 
neer did. 

Any ordinary ball-shaped water-filled carafe will act as a burning- 
glass. The ancients knew that and also noticed that the water didn't 
warm up in the process. There have been cases when a carafe of water 
inadvertently leH to stand in the sunlight on the sill of an oPen win- 
dow set .curtains and tablecloths on fire and charred tables. The 
big spheres of coloured water, which were traditionally used to adorn 
the show-windows of chemist's shops, now and again caused fires 
by igniting the inflammable substances stored nearby. 

A small round retort 12 cm in diameter is quite enough full of 
water will do to boil water in a watch glass. With a focal distance of 
15 cm (the focus is very close to the retort;, you can produce a tempera- 
ture of 120 C. You can light a cigarette with it just as easily as with a 
glass. One must note, however, that a glass lens is much more effective 
than a water-filled one, firstly, because the refractive index of water is 

149 



much less, and, secondly, because water intensively absorbs the infra- 
red rays which are so very essential for heating bodies. 

It is curious to note that the ancient Greeks were aware of the igni- 
tion effect of glass lenses a thousand odd years before eyeglasses and 
spyglasses were invented. Aristophanes speaks of it in his famous com* 
edy The Cloud. Socrates propounds the following] problem to Strop- 
tiadis: 

"Were one to write a promissory note on you for five talents, how 
would you destroy it? 

"Streptiadis: I have found a way which you yourself will admit to 
be very artful. I suppose you have seen the wondrous, transparent stone 
that burns and is sold at the chemist's? 

"Socrates: The burning-glass, you mean? 

"Strep tiadis: That is right. 

"Socrates: Well, and what? 

"Streptiadis: While the notary is writing I shall stand behind him 
and focus the sun on the promissory note and melt all ho writes. " 

I might explain that in Aristophanes 's days the Greeks used to write 
on waxed tablets which easily melted. 

ICE HELPS TO LIGHT FIRE 

Even ice, provided it is transparent enough, can serve as a convex lens 
and consequently ' as a burning-glass. Let] mo note, furthermore, that 
in this process the ice does not warm up and melt. Its refractive index 
is a wee bit less than that of water, and since a spherical water-filled 
vessel can be used as a burning-glass, so can a similarly shaped lump 
of ice. An ice "burning-glass " enabled Dr. Clawbonny in Jules Verne's 
The Adventures of Captain Hatleras to light a fire when the travellers 
found themselves stranded without a fire or anything to light it in terri- 
bly cold weather, with the mercury at 48 C below zero. 

"This is terrible ill-luck, 1 the captain said. 

44 * Yes,' replied the doctor. 

44 *We haven't oven a spyglass-to make a fire with! 1 

"'That's a great pity, ' the doctor remarked , 'because the sun is strong 
enough to light tinder.' 

ISO 



"We'll have to eat the boar raw, then,' said the captain. 

"'As a last resort, yes/ the doctor pensively replied. 'But why not.,.. 1 

"'What?' Hatteras inquired. 

"Tvc got an idea.' 

"'Then we're saved,' exclaimed the bosun. 

"'But...' the doctor was hesitant. 

"'What is it?' asked the captain. 

41 'We haven't got a burning-glass, but we can make one. 1 

"'How?' asked the bosuri. 

"'From a piece of ice!' 

"'And you think....' 

"'Why not? We must focus the sun's rays on the tinder and a piece 
of ice can do that. Fresh-water ice is hotter though it's more transpar- 
ent and less liable to break. 1 




Fig. 113. The doctor focusscd the sun's bright rays on 
the tinder" 




"'The ice boulder over there,' the bosun pointed to a boulder som 
hundred steps away, 'seems to be what wo need.' 
"'Yes. Take your axe and let's go.' 

"The three walked over to the boulder and found that it was indeed 
of fresh-water ice. 

"The doctor told the bosun to chop off a chunk of about a foot in diam- 
eter, and then he ground it down with his axe, his knife, and finally 
polished it with his hand and produced a very good, transparent burn- 
ing-glass. The doctor focussed the sun's bright rays on the tinder which 
began to blaze a few seconds later. " 

Jules Verne's story is not an im- 
possibility. The first time this was 
ever done with success was in Eng- 
land in 1763. Since then ice has been 
used more than once for the purpose. 
Fig. 114. A bowl for making an It is, of course, hard to believe that 
ice burning-glass one cou i ( ] ma ke an ice burning-glass 

with such crude tools as an axe and 

knife and "one's hand " in a frost of 48C below zero. There is, however, 
a much simpler way: pour some water into a bowl of the proper shape, 
freeze it, and then take out the ice by slightly heating the bottom of the 
bowl. Such a "burning-glass" will work only in the open air on a clear 
and frosty day. Inside a room behind closed windows it is out of the 
question, because the glass panes absorb much of the solar energy and 
what is left of it is not strong enough. 

HELPING SUNLIGHT 

Here is one more experiment which you can easily do in wintertime. 
Take two pieces of cloth of the same size, one black and the other white, 
and put them on the snow out in the sun. An hour or two later you will 
find the black piece half-sunk, while the white piece is still where it 
was. The snow melts sooner under the black piece because cloth of this 
colour absorbs most of the solar rays falling on it, while white clotk 
disperses most of the solar rays and consequently warms up much less. 

This very instructive experiment was first performed by Benjamin 

152 



Franklin, the American scientist of War for Independence fame, who 
won immortality for his invention of the lightning conductor, 

"I took a number of little square pieces of broad cloth from a tailor's 
pattern card, of various colours. There were black, deep blue, lighter 
blue, green, purple, red. yellow, white, and other colours, or shades of 
colours. I laid them all out upon the snow in a bright sunshiny morn- 
ing. In a few hours (I cannot now be exact as to the time), the black, 
being wanned most by the sun, was sunk so low as to he below the stroke 
of the sun's rays; the dark blue almost as low, the lighter blue not quite 
so much as the dark, the other colours less as they were lighter; and 
the quite white remained on the surface of the snow, riot having en- 
tered it at all. 

"What signifies philosophy that does not apply to some use? May 
we not learn from hence, that black clothes arc not so fit to wear in a hot 
sunny climate or season, as white ones; because in such clothes the body 
is more heated by the sun when we walk abroad, and we are at the same 
time heated by the exercise, which double heat is apt to bring on putrid 
dangerous fevers?... That summer hats for men or women' should be 
white, as repelling that heat which gives headaches to many, and to some 
the fatal stroke that the French call the coup de soleil?... That fruit 
walls being blacked may receive so much heat from the sun in the day- 
time, as to continue warm in some degree through the night, and there- 
by preserve the fruit from frosts, or forward its growth? with sun- 
dry other particulars of less or greater importance, that will occur from 
time to time to attentive minds? " 

The benefit that can be drawn from this knowledge was well illus- 
trated during the expedition to the South Pole that the Germans 
made aboard the good ship Haussin. 1903. The ship was jammed by ice- 
packs and all methods usually applied in such circumstances explo- 
sives and ice-saws proved abortive. Solar rays were then invoked. A 
two-kilometre long strip, a dozen metres in width, of dark ash and coal 
was strewn from the ship's bow to the nearest rift. Since this happened 
during the Antarctic summer, with its long and clear days, the sun was 
able to accomplish what dynamite and saws had failed to do. The ice 
melted and cracked all along the strip, releasing the ship from its 
clutches. 

153 



MIRAGES 

I suppose you all know what causes a mirage. The blazing sun heats 
up the desert sands and lends to them the property of a mirror because 
the density of the hot surface layer of air is less than the strata higher 
up. Oblique rays of light from a remote object meet this layer of air and 
curve upwards from the ground as if reflected by a mirror after striking 
it at a very obtuse angle. The desert-traveller thus thinks he is seeing a 
sheet of water which reflects the objects standing on its banks (Fig. 115). 




Fig. 115. Desert mirages explained. This drawing, usually given in textbooks, 
shows too steeply the ray's course towards the ground 

Rather should we say that the hot surface layer of air reflects not like a 
mirror but like the surface of water when viewed from a submarine. 
This is not an ordinary reflection but what physicists call total reflec- 
tion, which occurs when light enters the layer of air at an extremely 
obtuse angle, far greater than the one in the figure. Otherwise the "crit- 
ical angle" of incidence will not be exceeded. 

154 



Please note to avoid misunderstanding that a denser strata mu*t 
be above the rarer layers. However, we know that denser air is heavier 
and always seeks to descend to take the place of lighter lower layers and 
force them upwards. Why, in the case of a mirage, is the denser air above 
the rarer air? Because air is in constant motion. The heated surface 
air keeps on being forced up by a new replacing lot of heated air. This is 
responsible for some rarefied air always remaining just above the hot 
sand. It need not ( be the, same rarefied air a all the time but that is 
something that makes no difference to the rays. 

This phenomenon has been known from times immemorial. (A some- 
what different mirage appearing in the air at a higher level than the 
observer is caused by reflection in upper rarefied layers.) Most people 
think this classical type of mirage can be observed only in the blazing 
southern deserts and never in more northerly latitudes. They are wrong. 
This is frequently to be observed in summer on asphalted roads which, 
because they are dark, are greatly boated by the sun. The dull road's 
rnrface seems to look like a pool of water able to reflect distant objects. 
Fig. 116 shows the path light takes in this case. A sufficiently observ- 
ant person will see these mirages oftener than one might think. 

There is one more type of mirage a side one which people usually 
do not have the faintest suspicion about. This mirage, which has been 




Fig. JJG. Mirapc on paved highway 



described by a Frenchman, was produced 
by reflection from a heated sheer wall. As 
he drew near to the wall of a fortress he no- 
ticed it suddenly glisten like a polished 
mirror and reflect the surrounding land- 
scape. Taking a few steps he saw a similar 
change in another wall. He concluded that 
this was due to the walls having heated up 
considerably under the blazing sun. Fig. 117 
gives the position of the walls (F and F') 
and the spots (A and A') where the observ- 
er stood. 

The Frenchman found that the mirage re- 
curred every time the wall was hot enough 
and even managed to photograph the phe- 
nomenon. 

Fig 118 depicts, on the left, the fortress 
Fig. 117. Ground plan of wall F, which suddenly turned into the glis- 

Sas f secn SS WalT IfSSS tenin g mirror on the ri & ht " as Photographed 

polished from point A, and from point A'. The ordinary grey concrete 

wall F 1 from point A' WftU Qn the left naturally cannot reflect the 

two soldiers near it. But the same wall, miraculously transformed into 
a mirror on the right, does symmetrically reflect the closer of the two 
soldiers. Of course it isn't the wall itself that reflects him, but its surface 
layer of hot air. If on a hot summer day you pay notice to walls of 
big buildings, you might spot a mirage of this kind. 




"THE GREEN RAY" 

"Have you ever seen the sun dip into the horizon at sea? No doubt, 
you have. Have you ever watched it until the upper rim touches the 
horizon and then disappears? Probably you have. But have you ever 
noticed what happens on the instant when our brilliant luminary sheds 
its last ray provided the sky is a cloudless, pellucid blue? Probably 
not. Don't miss this opportunity. You will see, instead of a red ray, one 
of an exquisite green that no artist could ever reproduce and that nature 



156 




Fig. 118. Rough, grey wall (left) suddenly seems to act like 
a polished mirror (right) 

herself never displays either in the variously tinted plants or in the 
most transparent of seas." 

This note published in an English newspaper sent the young heroine 
of Jules Verne's The Green Ray in raptures and made her roam the world 
solely to see this phenomenon with her own eyes. Though, according to 
Jules Verne, this Scottish girl failed to see the lovely work of nature, 
still it exists It is no myth, though many legends are associated with 
it. Any lover of nature can admire it, provided he takes the pains to 
hunt for it. 

Where does the green ray or flash come from? Recall what you saw 
when you looked at something through a prism. Try the following. Hold 
the prism at eye level with its broad horizontal plane turned downwards 
and look through it at a piece of paper tacked to the wall You will see 
the sheet firstly loom and secondly display a violet-blue rim at the 
top and a yellow-red edge at the bottom. The elevation is due to refrac- 
tion, while the coloured rims owe their origin to the property of glass 

157 



to refract differently light of different colours. It bonds violets and blues 
more than any other colour. That is why we see a violet-blue rim on 
top. Meanwhile, since it bends reds least, the bottom edge is precisely 
of this colour. 

So that you comprehend my further explanations more easily, I 
must say something about the origin of these coloured rims. A prism 
breaks up the white light emitted by the paper into all the colours of 
the spectrum, giving many coloured images of the paper, disposed in 
the order of their refraction and often superimposed, one on the other. 
The combined effect of these superimposed coloured images produces 
white light (the composition of the spectral colours) but with coloured 
fringes at top and bottom. The famous poet Goethe who performed this 
experiment but failed to grasp its real meaning thought that he had 
debunked Newton's colour theorv. Later he wrote his own Theory of 
Colours which is based almost entirely on misconceptions. But I sup- 
pose you won't repeat his blunder and expect the prism to colour ev- 
erything anew. 

We see the earth's atmosphere as a vast prism of air, with its base 
facing us. Looking at the sun on the horizon we sec it through a prism 
of gas. The solar disc has a blue-green fringe on top and a yellow-red 
one at the bottom. While the sun is above the horizon, its disc's bril- 
liant colour outshines all other less bright bands of colour and we 
don't see them at all. But during the sunrises and sunsets, when practi- 
cally the entire disc of the sun is below the horizon, we may spot the 
blue double-tinted fringe on the upper rim, with an azure blue right on 
top and a paler blue produced by the mixing of green and blue be- 
low it. When the air near the horizon is clear and translucent, we see a 
blue fringe, or the "blue ray". But often the atmosphere disperses the 
blues and we see only the remaining green fringe the "green ray". 
However, most often a turbid atmosphere disperses both blues and greens 
and then we see no fringe at all, the setting sun assuming a crimson red. 

The Pulkovo astronomer G.A. Tikhov, who devoted a special mono- 
graph to the "green ray", gives us some tokens by which we may see it. 
"When the setting sun is crimson-huod and it doesn't hurt to look at it 
with the naked eye you may be sure that there will be no green flash. " 
This is clear enough: the fact of a red sun means that the atmosphere 

158 



intensively disperses blues and greens, or, in other words, the whole 
of the upper rim of the solar disc. "On the other hand, " he continues, 
"when the setting sun scarcely changes its customary whitish yellow 
and is very bright [in other words, when atmospheric absorption of light 
is insignificant Y.P.] you may quite likely expect the green flash. 
However, it is important for the horizon to be a distinct straight line 
with no uneven relief, forests or buildings. We have all those condi- 
tions at sea, which explains why seamen are familiar with the green 
flash. " 

To sum up: to see the "green ray", you must observe the sun when 
setting or rising and when the sky is extremely clear. Since the sky 
at the horizon in southern climes is much more translucent than in 
northern latitudes, one is liable to see the "green ray" there much of- 
tener. But neither in our latitudes is it so rare as many think most 
likely, I suppose, because of Jules Verne. You will detect the "green ray" 
sooner or later as long as you look hard enough. This phenomenon baa 
been seen even in a spyglass. 

Here is how two Alsatian astronomers describe it: 
"During the very last minute before the sun sets, when, consequently, 
a goodly part of its disc is still to be seen, a green fringe hems the waving 
but clearly etched outline of the sun's ball. But until the sun sets alto- 
gether, it cannot be seen with the naked eye. It will be seen only when 
the sun disappears completely below the horizon. However, should one 
use a spyglass with a powerful enough magnification of roughly 100 
one will sec the entire phenomenon very well. The green fringe is seen 
some ten minutes before the sun sets at the latest. It incloses the disc's 
upper half, while a red fringe hems the lower half. At first the fringe 
is extremely narrow, encompassing at the outset but a few seconds of an 
arc. As the sun sets, it grows wider, sometimes reaching as much as half 
a minute of an arc. Above the green fringe one may often spot similarly 
green prominences, which, as the sun gradually sinks, seem to slide along 
its rim up to its apex and sometimes break away entirely to shine inde- 
pendently a few seconds before fading" (Fig. 119). 

Usually this phenomenon lasts a couple of seconds. In extremely 
favourable conditions, however, it may last much longer. A case of more 
than 5 minutes has been registered; this was when the sun was setting 

159 




Fig. 119. Protracted observation of the "green ray"; it was seen beyond the moun- 
tain range for 5 minutes. Top right-hand corner: the "green ray" as seen in a spy- 
glass. The Sun's disc has a ragged shape. 1. The Sun's blinding glare prevents us 
from seeing the green fringe with the unaided eye. 2. The "green ray" can be scon 
with the unaided eye when the Sun has almost completely set 



behind a distant mountain and the quickly walking observer saw the 
green fringe as seemingly sliding down the hill (Fig. 119). 

The instances recorded when the "green ray" has been observed dur- 
in? a sunrise that is, when the upper rim of our celestial luminary peeps 
out above the horizon are extremely instructive, as they debunk the 
frequent suggestion that the phenomenon is presumably nothing more 
than an oDtical illusion to which the eye succumbs owing to the fatigue 
caused by looking at the brilliant setting sun. Incidentally, the sun is 
not the only celestial object lhat sheds the "green ray ". Venus has also 
produced it when setting. (You will find more about mirages and the 
green flash in M. Minaert's superb book Light and Colour in Nature.) 



CHAPTER NINE 

VISION 

BEFORE PHOTOGRAPHY WAS INVENTED 

Photography is so ordinary nowadays that we find it hard to imagine 
how our forefathers, even in the past century, got along without it. 
In his Posthumous Papers of the Pickwick Club Charles Dickens tells 
us the amusing story of how British prison officers took a person's 
likeness some hundred or so years ago. The action takes place in the 
debtors' prison where Pickwick has heen brought. Pickwick is told 
that he'll have to sit for his portrait. 

"'Sitting for my portrait!' said Mr. Pickwick. 

"'Having your likeness taken, sir,' replied the stout turnkey. 'We're 
capital hands at likeness here. Take 'em in no time, and always exact. 
Walk in, sir, and make yourself at home.' 

"Mr. Pickwick complied with the invitation, and sat himself down: 
when Mr. Weller, who stationed himself at the back of the chair, whis- 
pered that the sitting was merely another term for undergoing an in- 
spection by the different turnkeys, in order that they might know prison- 
ers from visitors. 

"'Well, Sam,' said Mr. Pickwick. 'Then] I wish the artists would 
come. This is rather a public place.' 

"'They won't be long, sir, I des-say,' replied Sam. 'There's a Dutch 
clock, sir.' 

"'So I see,' observed Mr. Pickwick. 

"'And a bird-cage, sir,' says Sam. 'Veels within veels, a prison in a 
prison. Ain't it, sir?' 

"As Mr. Weller made this philosophical remark, Mr. Pickwick was 
aware that his sitting had commenced. The stout turnkey having been 

112668 161 



relieved from the lock, sat down, and looked at him carelessly, from 
time to time, while a long thin man who had relieved him, thrust his hands 
beneath his coat-tails, and planting himself opposite, took a good long 
view of him. A third, rather surly-looking gentleman: who had apparent- 
ly been disturbed at his tea, for he was disposing of the last remnant of 
a crust and butter when he came in: stationed himself close to Mr. Pick- 
wick; and, resting his hands on his hips, inspected him narrowly; while 
two others mixed with the group, and studied his features with most 
intent and thoughtful faces. Mr. Pickwick winced a good deal under 
the operation, and appeared to sit very uneasily in his chair; but he 
made no remark to anybody while it was being performed, not even to 
Sam, who reclined upon the back of the chair, reflecting, partly on the 
situation of his master, and partly on the great satisfaction it would 
have afforded him to make a fierce assault upon all the turnkeys 
there assembled, one after the other, if it were lawful and peaceable 
so to do. 

"At length the likeness was completed, and Mr. Pickwick was in- 
formed, that ho might now proceed into the prison." 

Still earlier it was a list of "features" that did for such memorised 
"portraits". In his Boris Godunov, Pushkin tells us how Grigory Otrc- 
pyev was described in the tsar's edict: "Of short stature, and broad 
chest; one arm is shorter than the other; the eyes are blue and hair gin- 
ger; a wart on one cheek and another on the forehead. " Today we necdr '*. 
do that; we simply provide a photograph instead. 

WHAT MANY DON'T KNOW HOW TO DO 

Photography was introduced in Russia in the 1840's, first as daguerreo- 
typesprints on metal plates that were called so after their inventor, 
Dagucrre. It was a very inconvenient method; one had to pose for quite 
a long stretch for as long as fourteen minutes or more. "My grand- 
father," Prof. B.P. Wcinberg, the Leningrad physicist, told me, "had 
to sit for 40 minutes before the camera to get just one daguerreotype, 
from which, moreover, no prints could be made." 

Still the chance to have one's portrait made without the artist's in- 
tervention seemed such a wonderful novelty that it took the general 

162 



public quite a time to get used to the idea. One old Russian magazine 
for 1845 contains quite an amusing anecdote on the score: 

"Many still cannot believe that the daguerreotype acts by itself. One 
gentleman came to have his portrait done. The owner [the photographer 
Y.P.] begged him to be seated, adjusted the lenses, inserted a plate, 
glanced at his watch, and retired. While the owner was present, the gen- 
tleman sat as if rooted to the spot. But he had barely gone out when 
the gentleman thought it no longer necessary to sit still; he rose, took a 
pinch of snuff, examined the camera from every side, put his eye to the 
Ions, shook his head, mumbled, 'How ingenious,' and began to meander 
up and down the room. 

"The owner returned, stopped short in surprise at the doorway, and 
exclaimed: *What are you doing? I told you to sit still!* 

"'Well, I did. I got up only when you went out.' 

"'But that was exactly when you should have sat still. 9 

"'Why should I sit still for nothing?' the gentleman retorted." 

We're certainly not so naive today. 

Still, there are some things about photography that many do not know. 
Few, incidentally, know how one should look at a photograph. Indeed, 
it's not so simple as one might think, though photography has been in 
existence for more than a century now and is as common as could be. 
Nevertheless, even professionals don't look at photographs in the prop* 
er way. 

HOW TO LOOK AT PHOTOGRAPHS 

The camera is based on the same optical principle as our eye. Every- 
thing projected onto its ground -glass screen depends on the (distance 
between the lens and the object. The camera gives a perspective, which 
we would get with one eye note that! were our eye to replace the 
lens. So, if you want to obtain from a photograph the same visual im- 
pression that the photographed object produced, we must, firstly, look 
at the photograph with one eye only, and, secondly, hold it at the prop- 
er distance away, 

After all, when you look at a photograph with both eyes the picture 
you get is flat and not three-dimensional. This is the fault of our own 
vision. When we look at something solid the image it causes on the 

11* 163 



retina of either eye is not the same (Fig. 120). This is mainly why we 
see objects in relief. Our brain blends the two different images into one 
that springs into relief this is the basic principle of the stereoscope. 
On the other hand, if we are looking at something that is flat a wall, 
for instance both eyes get an identical sensory picture telling our brain 
that the object we are looking at is really flat. 

Now you should realise the mistake we make when 
we look at a photograph with both eyes. In this 
manner we compel ourselves to believe that the 
picture we have before us is flat. When we look 
with both eyes at a photograph which is really in- 
tended only for one eye, we prevent ourselves from 
as [seen separately seeing the picture that the photograph really shows, 
by the left and right anc [ thus destroy the illusion which the camera 
eye when held close , . , i_ * 

to the face* produces with such perfection. 




HOW FAR TO .HOLD A PHOTOGRAPH 

The second rule I mentioned that of holding the photograph at the 
proper distance away from the eye is just as important, for otherwise 
we get the wrong perspective. How far away should we hold a photo- 
graph? To recreate the proper picture we must look at the photograph 
from the same angle of vision from which the camera lens reproduced 
the image on the ground -glass screen, or in the same way as it "saw" 
the object being photographed (Fig. 121). Consequently, we must hold 
the photograph at such a distance away from the eye that would be as 
many times less the distance between the object and the lens as the size 
of the image on the photograph is less its actual size. In other words, 



Fig. 121. In a camera angle 1 is equal to angle 2 



we must hold the photograph at a distance which is roughly the same 
as the focal length of the camera lens. 

Since most cameras have a focal length of 12-15 cm (the author has 
in mind the cameras that were in use when he wrote his Physics for 
Entertainment Ed.), we shall never be able to get the proper distance 
for the photographs they give, as the focal length of a normal eye at best 
(25 cm) is nearly twice the indicated focal length of the camera lens. 
A photograph tacked on a wall also seems flat because it is looked at 
from a still greater distance away. Only the short-sighted with their 
short focal length of vision, as well as children, who are able to accom- 
modate their vision to see objects very close up, will be able to admire 
the effect that an ordinary photograph produces when we look at it 
properly with one eye, because when they hold a photograph 12-15 cm 
away, they get not a flat image but one in relief the kind of image a 
stereoscope produces. 

I suppose you will now agree with me in noting that it is only due to 
ignorance that we do not derive the pleasure a photograph can give, 
and that we often unjustly blame them for being lifeless. 

QUEER EFFECT OF MAGNIFYING GLASS 

The short-sighted easily see ordinary photographs in relief. What 
should people with normal eyesight do? Here a magnifying glass will 
help. By looking at photographs through a magnifying glass with a two- 
fold power, people with normal eyesight will derive the indicated advan- 
tage of the short-sighted, and see them in relief without straining their 
eyesight. 

There is a tremendous difference between the effect thus produced 
and the impression we get when we look at a photograph with both eyes 
from quite a distance. It almost amounts to the stereoscopic effect. Now 
we know why photographs often spring into relief when looked at with 
one eye through a magnifying glass, which, though a generally known 
fact, has seldom been properly explained. One reviewer of this book 
wrote'to me in this connection: 

"Please take up in a future edition the question of why photographs 
appear in relief when viewed through a magnifying glass. Because I con- 

165 



tend that the involved explanation provided of the stereoscope holds 
no water at all. Try to look in the stereoscope with one eye. The picture 
appears in relief despite all that theory has to say. " 

I am sure you will agree that this does not pick any holes in the theory 
of stereoscopic vision. 

The same principle lies at the root of the curious effect produced by 
the so-called panoramas, that are sold at toy shops. This is a small box, 
in which an ordinary photograph a landscape or a group of people is 
placed and viewed through a magnifying glass with one eye, which in 
itself already gives a stereoscopic effect. The illusion is usually en- 
hanced by some of the objects in the foreground being cut out and 
placed separately in front of the photograph proper. Our eye is very sen- 
sitive to the solidity of objects close by; as far as distant/ objects are 
concerned, the impression is much less perceptible. 

ENLARGED PHOTOGRAPHS 

Can we make photographs so that people with normal eyesight are 
able to see them properly, without using a magnifying glass? We can, 
merely by using cameras having lenses with along focal length. You al- 
ready know that a photograph obtained with the aid of a lens having a 
focal distance of 25-30 cm will appear in relief when viewed with one 
eye from the usual distance away. 

One can even obtain photographs that won't seem flat even when 
looked at with both eyes from quite a distance. You also know that our 
brain blends two identical retinal images into one flat picture. How- 
ever, the* greater the distance away from the object, the less our brain is 
able to do that. Photographs taken with the aid of a lens having a focal 
distance of 70 cm can be looked at with both eyes without losing the 
sense of depth. 

Since it is incommoding to resort to such lenses, let me suggest anoth- 
er method, which is to enlarge the picture you take with any ordinary 
camera. This increases the distance at which you should look at photo- 
graphs to get the proper effect. A four- or fivefold enlargement of a pho- 
tograph taken with a 15 cm lens is already quite enough to obtain the 
desired effect you can look at it with both eyes from 60 to 75 centime- 

166 



tres away. True, the picture will bo a bit blurred but this is barely 
discernible at such a distance. Meanwhile, as far as the stereoscopic 
effect and depth are concerned, you only stand to gain. 

BEST SEAT IN MOVIE-HOUSE 

Cinema-goers have most likely noticed that some films seem to spring 
into unusually clear relief to such an extent at times that one seems 
to see real scenery and real actors. This depends not on the film, as is 
often thought, but on where you take your seat. Though motion pictures 
are taken with cameras having lenses with a very short focal length, 
their projection on the screen is a hundred times larger and you can 
see them with both eyes from quite a distance (10 crnX 100 = 10 ni). 
The effect of relief is best when you look at the picture from the same 
angle of vision as the movio camera "looked" when it was shooting the 
film. 

How should one find the distance corresponding to such an optimal 
angle of vision? Firstly, one must choose a seal right opposite the middle 
of the screen. Secondly, one's seat must be away from the screen at a dis- 
tance which is as many times the screen's width as the focal length of 
the movie-camera lens is greater than the width of the film if self. Movie- 
camera lens usually have a focal length of 35 mm, 50 mm, 75 mm, or 
100 mm, depending on the subject being shot. The standard width of 
film is 24 mm. For a focal length of 75 mm, for instance, we get the pro- 
portion: 

the distance focal length 75 

screen width M "01in" width ""^ 2~4 ^^ 

So, to find how far away you should seat yourself from the screen, you 
should multiply the width of the screen, or rather the projection onto 
the screen, by three. If the width is six of your steps, then the best seat 
would be 18 steps away from the screen. Keep this in mind when try- 
ing various devices offering a stereoscopic effect, because rmr> pay oa 
ly ascribe to the invention what is really due to the < 
tioned. 



FOR READERS OF PICTORIAL MAGAZINES 

Reproductions in books and magazines naturally have the same prop- 
erties as the original photographs from which they were made; they 
also spring into relief when looked at with one eye from the proper dis- 
tance. But since different photographs are taken by cameras having lenses 
with different focal lengths, one can find the proper distance only by 
trial and error. Cup one eye with your hand and hold the illustration at 
arm's length. Its plane must be perpendicular to the line of vision and 
your open eye must be right opposite the middle of the picture. Gradual- 
ly bring the picture closer, steadily looking at it meanwhile; you easily 
catch the moment when it appears in clearest relief. 

Many illustrations that seem blurred and flat when you look at them 
in your habitual way acquire depth and clearness when viewed as' I 
suggest. One will even catch the sparkle of water and other such purely 
stereoscopic effects. 

It's amazing that few people know these simple things though they 
were all explained in popular-science books more than half a century 
ago. In his Principles of Mental Physiology, with Their Application 
to the Training and Discipline of the Mind, and the Study of Its Mor- 
bid Conditions, William Carpenter has the following to say about how 
one should look at photographs. 

"It is remarkable that the effect of this mode of viewing photographic 
pictures is not limited to bringing out the solid forms of objects; for 
other features are thus seen in, a manner more true to the reality, and 
therefore more suggestive of it. This may be noticed especially with re- 
gard to the representation of still water ', which is generally one of the 
most unsatisfactory parts of a photograph; for although, when looked 
at with 60/Acyes, its surface appears opaque, like white wax, a wonder- 
ful depth and transparence are often given to it by viewing it with only 
one. And the same holds good also in regard to the characters of surfaces 
from which light is reflected as bronze or ivory; the material of the 
object from which the photograph was taken being recognised much 
more certainly when the picture is looked at with one eye, than when 
both are used (unless in stereoscopic combination)." 

There is one more thing we must note. Photographic enlargements, 

168 



as we have seen, aru more lifelike; photographs of a reduced size are 
not. True, the smaller-size photograph gives a better contrast; but it 
is flat and fails to give the effect of depth and relief. You should now be 
able to say why: it also reduces the corresponding perspective which 
is usually too little as it is. 



HOW TO LOOK AT PAINTINGS 

All I have said of photographs applies in some measure to paintings 
as well. They appear best also at the proper distance away, for only 
then do they spring into relief. It is better, too, to view them with but 
one eye, especially if they are small. 

"It has long been known," Carpenter wrote in the same book, "that if 
we gaze steadily at a picture, whose perspective projection, lights 
and shadows, and general arrangement of details, are such as accurately 
correspond with the reality which it represents, the impression it 
produces will bo much more vivid when we look with one eye only, 
than when we use both; and that the effect will be further heightened, 
when we carefully shut out the surroundings of the picture, by looking 
through a tube of appropriate size and shape. This fact has been com- 
monly accounted for in a very erroneous manner. 'We see more ex- 
quisitely/ says Lord Bacon, 'with one eye than with both, because the 
vital spirits thus unite themselves the more and become the stronger'; 
and other writers, though in different language, agree with Bacon 
in attributing the result to the concentration of the visual power, when 
only one eye is used. But the fact is, that when we look with both eyes 
at a picture within a moderate distance, we arc forced to recognise it 
as a flat surface; whilst, when we look with only one, our minds are at 
liberty to be acted on by the suggestions furnished by the perspective, 
chiaroscuro, etc.; so that, after we have gazed for a little time, the 
picture may begin to start into relief, and may even come to possess 
the solidity of a model." 

Reduced photographic reproductions of big paintings often give 
a greater illusion of relief than the original. This is because the reduced 
size lessens the ordinarily long distance from which the painting should 
be looked at, and so the photograph acquires relief, even close up. 

169 



THREE DIMENSIONS IN TWO 

All I have said about looking at photographs, paintings and drawings, 
while being true, should not be taken in the sense that there is no 
other way of looking at flat pictures to get the effect of depth and relief. 
Every artist, whatever his field painting, the graphic arts, or photo- 
graphy strives to produce an impression on the spectator regardless 
of his "point of view". After all he can't count on everybody viewing 
his creations with hands cupped over one eye and sizing up the distance 
for every piece. 

Every artist, including the photographer, has an extensive arsenal 
of means to draw upon to give in two dimensions objects possessing 
three. The different retinal images produced by distant objects are not 
the only token of depth. The "aerial perspective" painters employ 
grading tones and contrasts to make the background blurred and seem- 
ingly veiled by diaphanous mist of air, plus their use of linear per- 
spective produces the illusion of depth. A good specialist in art pho- 
tography will follow the same principles, cleverly choosing lighting, 
lenses, and also the appropriate brand of photographic paper to produce 
perspective. 

Proper focussing is also very important in photography. If the fore- 
ground is sharply contrasted and the remoter objects are "out of focus", 
this alone is already enough, in many cases, to create the impression 
of depth. On the contrary, when you reduce the aperture and give both 
foreground and background in the same contrast, you achieve a flat 
picture with no depth to it. Generally speaking, the effect a picture 
produces on the spectator thanks to which he sees three dimensions 
in two, irrespective of physiological conditions for visual perception 
and sometimes in violation of geometrical perspective depends large- 
ly, of course, on the artist's talent. 

STEREOSCOPE 

Why is it that we see solid objects as things having three dimensions 
and not two? After all the retinal image is a flat one. So why do we get 
a sensory picture of geometrical solidity? For several reasons. Firstly, 
the different lighting of the different parts of objects enables us to per- 

170 



ceive their shape. Secondly, the strain we feel when accommodating 
our eye to get a clear perception of the different distance of the object's 
different parts also plays a role; this is not a flat picture in which every 
part of the object depicted is set at the same distance away. And third- 
ly the most important cause is that the two retinal images are differ- 
ent, which is easy enough to demonstrate by looking at some close ob- 
ject, shutting alternately the right and left eye (Figs. 120 and 122). 




XL 



1 



Fig. 122. A spotted glass cube as seen with the 
left and right eye 

Imagine now two drawings of one and the same object, one as seen 
by the left eye, and the other, as seen by the right eye. If we look at 
them so that each eye sees only its "own" drawing, we get instead of 
two separate flat pictures one in relief. The impression of relief is great- 
er even than the impression produced when] we look at a solid object 
with one eye only. 

There is a special device, called the stereoscope, to view these pairs. 
Older types of stereoscopes used mirrors and the later models convex 
glass prisms to superimpose the two images. In the prisms which 
slightly enlarge the two images, because they are convex the light 
coming from the pair is refracted in such a way that its imagined 
continuation causes this superimposition. 

As you see, the stereoscope's basic principle is extremely simple; 
all the more amazing, therefore, is the effect produced. I suppose most 
of you have seen various stereoscopic pictures. Some may have used 
the stereoscope to learn stereometry more easily. However, I shall pro- 
ceed to tell you about applications of the stereoscope which I pre- 
sume many of you do not know. 



171 



BINOCULAR VISION 

Actually wo can provided we accustom our eyes to it dispense 
with the stereoscope to view such pairs, and achieve the same effect, 
with the sole difference that the image will not be bigger than it usually 
is in a stereoscope. Wheatstone, the inventor of the stereoscope, made 
use of this arrangement of nature. Provided here are several stereoscop- 
ic drawings, graded in difficulty that I would advise you to try 
viewing without a stereoscope. Remember that you will achieve results 

only if you exercise. (Note that not 
all can see storeoscopically, even in 
a stereoscope: some the squint-eyed 
or people used to working with one 
eye are utterly incapable of adjust- 
ment to binocular vision; others 
achieve results only after prolonged 
exercise. Young people, however, 
quickly adapt themselves, after a 
quarter of an hour.) 

Start with Fig. 123 which depicts 

two black dots. Stare several seconds at the space between them, 
meanwhile trying to look at an imagined object behind. Soon you 
will be seeing double, seeing four dots instead of two. Then the two 



Fig. 123. Stare at the space between 
the two dots for several seconds. 
The dots seom to merge 





Fig. 124. Do the same, after 
which turn to the next exercise 



Fig. 125. When these images 
merge you will see something 
like the inside of a pipe reced- 
ing into the distance 



extreme dots will swing far apart, while the two innermost dots will 
close up and become one. Repeat with Figs. 124 and 725 to see some- 
thing like the inside of a long pipe receding into the distance. 



172 



Then turn to Fig. 126 to see geometrical bodies seemingly suspended 
in mid-air. Fig. 127 will appear as a long corridor or tunnel. Fig. 128 
will produce the illusion of transparent glass in an aquarium. Finally, 
Fig. 129 gives you a complete picture, a seascape. 




o 







Fig. 126. When these four geometrical bodies merge, 
they seem to hover in mid-air 





Fig. 127. This pair gives a long corridor receding into 
the distance 

It is easy to achieve results. Most of my friends learned the trick 
very quickly, after a few tries. The short-sighted and far-sighted needn't 
take off their glasses; they view the pairs just as they look at any pic- 

173 



ture. Catch the proper distance at which they should bo held by trial 
and error. See that the lighting is good this is important. 

Now you can try to view stereoscopic pairs in general without a 
stereoscope. You might try the pairs in Figs. 130 and 133 first. Don't 




Fig. 128. A fish in an aquarium 




Fig. 129. A stereoscopic seascape 

overdo this so as not to strain your eyesight. If you fail to acquire 
the knack, you may use lenses for the far-sighted to make a simple but 
quite serviceable stereoscope. Mount them side by side in a piece of 
cardboard so that only their inner rims are available for viewing. 
Partition off the pairs with a diaphragm. 

174 



WITH ONE EYE AND TWO 

Fig. 130 (the upper left-hand corner) gives two photographs of 
three bottles of presumably one and the same size. However hard you 
look you cannot detect any difference in size. But there is a difference, 
and, moreover, a significant one. They seem alike only because they 
are not set at one and the same distance away from the eye or camera. 
The bigger bottle is further away than the smaller ones. But which 
of the three is the bigger bottle? Stare as much as you may, you will 
never get the answer. But the problem is easily solved by using a stereo- 
scope or exercising binocular vision. Then you clearly see that the left- 
hand bottle is furthest away, and the right-hand bottle closest. The 
photo in the upper right-hand corner shows the real size of the bottles. 

The stereoscopic pair at the bottom of Fig. 130 provides a still bigger 
teaser. Though the vases and candlesticks seem identical there is a 
great difference in size between them. The left-hand vase is nearly 
twice as tall as the right-hand one, while the left-hand candlestick, 
on the contrary, is much smaller than the clock and the right-hand 
candlestick. Binocular vision immediately reveals the cause. The 
objects are not in one row; they are placed at different distances, with 
the bigger objects being further away than the smaller articles. A fine 
illustration of the great advantage of binocular "two-eyed" vision 
over "one-eyed" vision! 

DETECTING FORGERY 

Suppose you have two absolutely identical drawings, of two equal 
black squares, for instance. In the stereoscope they appear as one square 
which is exactly alike either of the twin squares. If there is a white 
dot in the middle of each square, it is bound to show up on the square 
in the stereoscope. But if you shift the dot on one of the squares slight- 
ly off centre, the stereoscope will show one dot however, it will appear 
either in front of, or beyond, the square, not on it. The slightest of 
differences already produces the impression of depth in the stereoscope. 
This provides a simple method for revealing forgeries.; You need 
only put the suspected bank-bill next to a genuine one in a stereoscope, 
to detect the forged one, however cunningly made. The slightest dis- 

176 



cropanoy, oven in one toony-wcony lino, will strike the eye at onco 
appearing either in front of, or behind, the banknote. (The idea, which 
was first suggested by Dove in the mid-1 9th century, is not appli- 
cablefor reasons of printing technique to all currency notes issued 
today. Still his method will do to distinguish between two proofs 
of a book-page, when one is printed from newly-composed type.) 

AS GIANTS SEE IT 

When an object is very far away, more than 450 metres distant, the 
stereoscopic impression is no longer perceptible. After all the 6 cen- 
timetres at which our eyes are set apart are nothing compared with 
such a distance as 450 metres. No wonder buildings, mountains, and 
landscapes that are far away seem flat. So do the celestial objects 
all appear to be at the same distance, though, actually, the moon 
is much closer than the planets, while the planets, in turn, arc very 
much closer than the fixed stars. Naturally, a stereoscopic pair thus 
photographed will not produce the illusion of relief in the stereoscope. 

There is an easy way out, however. Just photograph distant objects 
from two points, taking care that they bo further apart than our two 
eyes. The stereoscopic illusion thus produced is one that we would got 
\\ore our eyes set much further apart than they really are. This is 
actually how stereoscopic pictures of landscapes are made. Thoy are 
usually viewed through magnifying (convex) prisms and the effect is 
most amazing. 




a ii 

Fig. 131. Tclestcrcoscope 



122668 



You have probably guessed that we could arrange two spyglasses to 
present the surrounding scenery in its real relief. This instrument, 
called a telestereoscope, consists of two telescopes mounted further 
apart than eyes normally arc. The two images arc superimposed by 
means of reflecting prisms (Fig. 131). 

Words fail to convey the sen- 
sation one experiences when look- 
ing through a telostereoscope, it 
is so unusual. Nature is trans- 
formed; distant mountains spring 
into relief; trees, rocks, buildings 
and ships at sea appear in all three 
dimensions. No longer is everything 
flat and fixed; the ship, that seems 
a stationary spot on the horizon 
in an ordinary spyglass, is moving. 
That is most likely how the legenda- 
ry giants saw surrounding nature. 
When this device has a tenfold 
power and the distance between its 
lenses is six times the interocular 
distance (6.5x6=39 cm), the jm- 




Fig. 132. Prism binoculars 



pression of relief is enhanced GO-fnN 
(b'X 10), compared with the impressi- 
on obtained by the naked eye. Even 

objects 25 kilometres away still appear in discernible relief. For land sur- 
veyors, seamen, gunners and travellers this instrument is a godsend, es- 
pecially if equipped with a range-finder. The Zeiss prism binoculars 
produces the same effect, as the distance between its lenses is greater than 
the normal interocular distance (Fig. 132). The opera glass, on the con- 
trary, has its lenses set not so far apart, to reduce the illusion of relief 
so that the decor and settings present the intended impression. 



178 



UNIVERSE IN STEREOSCOPE 

If we direct our leleslcreoscope at the moon or any other celestial 
object we shall fail to obtain any illusion of relief at all. This is only 
natural, as celestial distances are too big even for such instruments. 
After all, the 30-50 cm distance between the two lenses is nothing 
compared with the distance from the earth to the planets. Even if Iho 
two telescopes were mounted tens and hundreds of kilometres apart, 
we would get no results, as the planets are tens of millions of kilome- 
tres away. 

This is where stereoscopic photography steps in. Suppose we photo- 
graph a planet today and take another photograph of it tomorrow. 
Both photographs will be taken from one and the same point on tho 
globe, but from different points in the solar system, as in the space of 
24 hours the earth will have travelled millions of kilometres in orbit. 
Hence the two photographs won't be identical. In the stereoscope, tlio 
pair will produce the illusion of relief. As you see, it is the earth's orb- 
ital motion that enables us to obtain stereoscopic photographs of 
celestial objects. Imagine a giant with a head so huge that its inter- 
ocular distance ranges into millions of kilometres; this will give you 
a notion of the unusual effect astronomers achieve by such stereoscopic 
photography. Stereoscopic photographs of the moon present its moun- 
tains in relief so distinct that scientists have even been able to 
measure their height. It seems as if the magic chisel of some super- 
colossal sculptor has breathed life into the moon's flat and lifeless 
Scenery. 

The stereoscope is used today to discover the asteroids which swarm 
between the orbits of Mars and Jupiter. Not so long ago the astronomer 
considered it a stroke of good fortune if he was able to spot one of thcso 
asteroids. Now it can be done by viewing stereoscopic photographs 
of this part of space. The stereoscope immediately reveals the asteroid; 
it "sticks" out. 

In the stereoscope we can detect the difference not only in the po- 
sition of celestial objects but also in their brightness. This provides the 
astronomer with a convenient method for tracking down the so-called 
variable stars whose light periodically fluctuates. As soon as a star 

12* 179 



exhibits a dissimilar brightness the stereoscope detects at once the star 
possessing that varying light. 

Astronomers have also been able to take stereoscopic photographs 
of the nebulae (Andromeda and Orion). Since the solar system is too 
small for taking such photographs astronomers availed themselves of 
our system's displacement amidst the stars. Thanks to this motion 
in the universe we always see the starry heavens from new points. 
After the lapse of an interval long enough, this difference may even 
be detected by the camera. Then we can make a stereoscopic pair, and 
view it in the stereoscope. 

THREE-EYED VISION 

Don't think this a slip of the tongue on my part; T really mean Ihroe 
eyes. But how can one see with three eyes? And can oiie really acquire 
a third eye? 

Science cannot give you or mo a third eye, but it can give us the 
magic power to see an object as it would appear to a three-eyed crea- 
ture. Let me note first that a one eyed man can get from stereoscopic 
photographs that impression of relief which he can't and doesn't get 
in ordinary life. For this purpose we must project onto a screen in 
rapid sequence the photographs intended for right and left eyes that 
a normal person sees with both eyes simultaneously. The net result 
is the same because a rapid sequence of visual images fuses into one 
image just as two images seen simultaneously do. (It is quite likely that 
the surprising "depth" of movie films at times, in addition to the 
causes mentioned, is due also to this. When the movie camera sways 
with an "even motion as often happens because of the film-winder 
the still* will not be identical and, as they rapidly flit onto the screen 
will appear to us as one 3-dimensional image.) 

In that case couldn't a two-eyed person simultaneously watch a 
rapid sequence of two photographs with one eye and a third photograph, 
taken from yet another angle, with the other eye? Or, in other words, 
a stereoscopic "trio"? We could. One eye would get a single image, 
but in relief, from a rapidly alternating stereoscopic pair, while the 
other eye would look at the third photograph. This "three-eyed " vision 
enhances the relief to the extreme. 

180 



STEREOSCOPIC SPARKLE 

The stereoscopic pair in Fig. 133 depicts polyhedrons, one in white 
against a black background and the other in black against a white back- 
ground. How would they appear in a stereoscope? This is what Helm- 
holtz says: 

"When you have a certain plane in white on one of a stereoscopic 
pair and in black on the other, the combined image seems to sparkle, 




Fig. 133. Stereoscopic sparkle. In the stereoscope this pair produces 
a sparkling crystal against a black background 

even though the paper used for the pictures is dull. Such stereoscopic 
drawings of models of crystals produce the impression of glittering 
graphite. The sparkle of water, the glisten of leaves and other such 
things are still more noticeable in stereoscopic photographs when this 
is done. " 

In an old but far from obsolete book, The Physiology of the Senses. 
Vision, which the Russian physiologist Sechenov published in 1867, 
we find a wonderful explanation of this phenomenon. 

"Experiments artificially producing stereoscopic fusion of different- 
ly lighted or differently painted surfaces repeat the actual conditions 
in which we see sparkling objects. Indeed, how does a dull surface differ 
from a glittering polished one? The first one reflects and diffuses light 
and so seems identically lighted from every point of observation, 
while the polished surface reflects light in but one definite direction. 



13-2668 



181 



Therefore you can have instances when with one eye you get many re- 
flected rays, and with the other practically none these are precisely 
the conditions that correspond to the stereoscopic fusion of a white 
surface with a black one. Evidently there are bound to be instances 
in looking at glistening polished surfaces when reflected light is 
unevenly distributed between the eyes of the observer. Consequently, 
the stereoscopic sparkle proves that experience is paramount in the 
act during which images fuse bodily. The conflict between the fields of 
vision immediately yields to a firm conception, as soon as the expe- 
rience-trained apparatus of vision has the chance to attribute the 
difference to some familiar instance of actual vision." 

So the reason we see things sparkle OT at least one of the reasons 
is that the two retinal images are not the same. Without the stereoscope 
we would have scarcely guessed it. 

TRAIN WINDOW OBSERVATION 

I noted a little earlier that different images of one and the same 
object produce the illusion of relief when in rapid alternation they 
perceptibly fuse. Does this happen only when we sec moving images 
and stand still ourselves? Or will it also take place when the images 
are standing still but we are moving? Yes, we get the same illusion, as 
was only to be expected. Most likely many have noticed that movies 
shot from an express train spring into unusually clear relief just as good 
as in the stereoscope. If we pay heed to our visual perceptions whea 
riding in a fast train or car we shall see this ourselves. Landscapes 
thus observed spring into clear relief with the foreground distinctly 
separate from the background. The "stereoscopic radius" of our eyes 
increases appreciably to far beyond the 450-metre limit of binocular 
vision for stationary eyes. 

Doesn't this explain the pleasant impression we derive from a land- 
scape when observing it from the window of an express train? Remote 
objects recede and we distinctly see the vastness of the scenic pano- 
rama unfolding before us. When we ride through a forest we stereoscop* 
ically perceive every tree, branch, and leaf; they do not blend into 
one flat picture as they would to a stationary observer. On a mountain 

182 



road fast driving again produces the same effect. We seem to sense tan- 
gibly the dimensions of the hills and valleys. 

One-eyed people will also see this and I'm sure it will afford a star- 
tlingly novel sensation, as this is tantamount to the rapid sequence 
of pictures producing the illusion of relief, a point mentioned before. 
(This, incidentally, accounts for the noticeable stereoscopic effect pro- 
duced by movie films shot from a train taking a bend, when the ob- 
jects being photographed lie in the radius of this bend. This track "effect" 
is well-known to cameramen.) 

It is as easy as pie to check my statements. Just be mindful of your 
visual perceptions when riding in a car or a train. You might also no- 
tice another amazing circumstance which Dove remarked upon some 
hundred years ago what is well forgotten is indeed novel I that the 
closer objects flashing by seem smaller in size. The cause has little to 
do with binocular vision. It's simply because our estimate of distance 
is wrong. Our subconscious mind suggests that a closer object should 
really be smaller than usually, to seem as big as always. This is Helm- 
holtz's explanation. 

THROUGH TINTED EYEGLASSES 

Looking through red-tinted eyeglasses at a red inscription on white 
paper you see nothing but a plain red background. The letters disap- 
pear entirely from view, merging with the red background. But look 
through the same red-tinted glasses at blue letters on white paper and 
the inscription distinctly appears in black again on a red back- 
ground. Why black? The explanation is simple. Red glass does not 
pass blue rays; it is red because it can pass red rays only. Consequently, 
instead of the blue letters you see the absence of light, or black letters. 

The effect produced by what are called colour anaglyphs the same as 
produced by stereoscopic photographs is based precisely on this prop- 
erty of tinted glass. The anaglyph is a picture in which the two stereosco- 
pic images for the right and left eye respectively are superimposed] the 
two images are coloured differently one in blue and the other in red. 

The anaglyphs appear as one black but three-dimensional image 
when viewed through differently-tinted glasses. Through the red glass 

13* 183 



the right eye sees only the blue image the one intended for the right 
eye and sees it, moreover, in black. Meanwhile the left eye sees 
through the blue glass only the red image which is intended for the left 
eye again in black. Each eye sees only one image, the one intended 
for it. This repeats the stereoscope and, consequently, the result is the 
same the illusion of depth. 

"SHADOW MARVELS" 

The "shadow marvels" that were once shown at the cinemas are 
also based on the above-mentioned principle. Shadows cast by moving 
figures on the screen appear to the viewer, who is equipped with differ- 
ently-tinted glasses, as objects in three dimensions. The illusion is 
achieved by bicoloured stereoscopy. The shadow-casting object is 
placed between the screen and two adjacent sources of light, red and 
green. This produces two partially superimposed coloured shadows 
which are viewed through viewers matching in colour. 

The stereoscopic illusion thus produced is most amusing. Things 
seem to fly right your way; a giant spider creeps towards you; and 
you involuntarily shudder or cry out. The apparatus required is extreme- 
ly simple. Fig. 134 gives the idea. In this diagram G and R stand for 



PC 



^ \\ 



rm 



/ ^ 

X *.-" 



-"'"" \N 




Fig. 134. The "shadow marvel" explained 



the green and red lamps (left); P and Q represent the objects placed 
between the lamps and screen; pG, qG, pR and qR are the tinted shad- 
ows that these objects cast on the screen; P l and Q l show where the 
viewer looking through the differently-tinted glasses G is the green 
glass, and R 9 the red one sees these objects. When the "spider" behind 
the screen is shifted from Q to P the viewer thinks it to be creeping from 
& to P t . 

Generally speaking, every time the object behind the screen is moved 
towards the source of light, thus causing the shadow cast on the screen 
to grow larger, the viewer thinks the object to be moving from the screen 
towards him. 

Everything the viewer thinks is moving towards him from the screen 
is actually moving on the other side of the screen in the oppo- 
site directionfrom the screen to the source of light. 

MAGIC METAMORPHOSES 

I think it would be appropriate at this stage to describe a series of 
illuminating experiments conducted at the Science for Entertainment 
Pavilion of a Leningrad recreation park. A corner of the pavilion was 
furnished as a parlour. Its furniture was covered with dark-orange 
antimacassars, the table was laid with green baize, on which there 
stood a decanter full of cranberry juice and a vase with flowers in it, 
and there was a shelf full of books with coloured inscriptions on their 
bindings. 

The visitors first saw the "parlour" lit by ordinary white electric 
light. When the ordinary light was turned off and a red light switched 
on in its stead, the orange covers turned pink and the green tablecloth 
a dark purple; meanwhile the cranberry juice lost its colour and looked 
like water; the flowers in the vase changed in hue and seemed different; 
and some inscriptions on the bookbindings vanished without trace. 
Another flick of the switch and a green light went on. The "parlour" 
was again transformed beyond recognition. 

These magic metamorphoses will illustrate Newton's theory of col- 
our, the gist of which is that a surface always possesses the colour of 
the rays it diffuses, rather than of the rays it absorbs. This is how New- 

185 



ton's compatriot, the celebrated British physicist John Tyndall, formu- 
lates the point. 

"Permitting a concentrated beam of white light to fall upon fresh 
leaves in a dark room, the sudden change from green to red, and from 
red back to green, when the violet glass is alternately introduced and 
withdrawn, is very surprising ... question of absorption." 

Consequently the green tablecloth shows up as green in white light 
because it diffuses primarily the rays of the green and adjacent spectral 
bands and absorbs most of all the other rays. If we direct a mixed rod 
and violet light at this green tablecloth, it will diffuse only the violet 
and absorb most of the red, thus turning purple. This is the main ex* 
planation for all the other colour metamorphoses in the "parlour". 

But why does the cranberry juice lose all colour when a red light is 
directed at it? Because the decanter stands on a white runner laid across 
the green baize. Once we remove the runner the cranberry juice turns 
red. It loses its colour (in red lighting) only against the background 
of the runner, which, though it turns red, we ourselves continue to regard 
as white, both by force of habit and due to the contrast it presents to 
the purple tablecloth. Since the juice has the same colour as the runner, 
which we imagine to be white, we involuntarily think the juice to be 
white too. That is why it appears no longer as red juice but a^colour- 
less water. You may derive the same impressions by viewing the sur- 
roundings through tinted glasses. (See my Do You Know Your Physics? 
for more about this effect.) 

HOW TALL IS THIS BOOK? 

Ask a friend to show you how high the book he is holding would be 
from the floor, if he stood it up on one edge. Then check his statement. 
He is sure to guess wrongly: the book will actually be half as tall. Fuis 
therm ore, better ask him not to bend down to show how high the book 
would come up to, but provide the answer in so many words, with you 
assisting. You can try this with any other familiar object a table 
lamp, say, or a hat. However, it should be one you have grown ac- 
customed to seeing at the level of your eyes. The reason why people err 
is because every object diminishes in size when looked at edgeways. 

186 



TOWER CLOCK DIAL 



We constantly make the same mistake when we try to estimate the 
size of objects that are way above our heads, especially tower clocks. 
Even though we know that these clocks are very large, our estimates 
of their size are much less than the actual size. Fig. 1S5 shows how large 
the dial of the famous Westmin- 
ster Tower clock in London looks 
when brought down to the road 
below. Ordinary human beings 
look like midgets next to it. 
Still it fits the orifice in the clock 
tower shown in the distance be- 
lieve it or not! 

BLACK AND WHITE 

Look from afar at Fig. 136 and 
say how many black spots would 
fit in between the bottom spot 
and any of the top spots. Four 
or five? I daresay your answer 
will be: "Well, there's not 
enough room for five but there's 
certainly enough for four." 

Believe it or not you can 
check it! there's just enough 

room for three, no more! This illusion, owing to which dark patches seem 
smaller than white patches of the same size, is known as "irradiation". 
This comes from an imperfection of our eye, which, as an optical instru- 
ment, does not quite measure up to strict optical requirements. Its 
refrangible media do not cast on the retina that sharply-etched outline 
which one gets on the ground-glass screen of a weli-focussed camera. 
Owing to what is called spherical aberration, every light patch has 
a light fringe which enlarges the retinal image. That is why light areas 
always seem bigger than dark areas of equal size. 







Fig. 136. The size of the Westminster 
Tower clock 



187 






In his Theory of Colours the great poet Goethe who, though an observ- 
ant student of nature, was not always a prudent enough physicist has 
the following to say about this phenomenon: 

"A dark object seems smaller than a light ob- 
ject of the same size. If we look simultaneously 
at a white spot on a black background and at a 
black spot of the same diameter but against a 
white background, the latter will seem about a 
fifth smaller than the former. If we render the 
black spot correspondingly larger, the two spots 
will seem identical. The crescent moon seems 
part of a circle the diameter of which would be 
larger than that of the moon's darker portion 
which we sometimes see [the ashen light wit- 
nessed when the "old moon is in the new moon's 
arms" Y. P.]. In dark dress we seem slimmer 
than in clothes of light tones. Light coming 
over the rim of something seems to make a de- 
pression in it. A ruler from behind which we see a 
candle flame seems to have a notch in it at this 
point. The rising and setting sun seem to make 
a depression in the horizon." 
Goethe was right on every point, with the sole exception that a 
white spot does not always seem larger than a black spot of equal size 
by one and the same fraction. This depends solely on from how far away 
you look at the spots. Why? Just move Fig. 136 still further away. 
The illusion is still more striking, because the additional fringe we 
mentioned is always of the same width. Close up, the fringe enlarges 
the white area by 10%; further away, it takes up from 30 to even 
50% of the white area, because the actual image of the spot is already 
smaller itself. This also explains why we see the circular white spots 
in Fig. 137 as hexagons when viewed from two or three steps away. 
From six to eight steps away this figure will already seem a typical 
honeycomb. 

To say that irradiation is responsible for this illusion is an explana- 
tion that has not quite satisfied me, ever since I noticed that black dots 



Fig. 136. The gap 
between the bottom 
spot and each of the 
top two seems more 
than the distance be- 
tween the outer edges 
of the two top spots. 
Actually, they are 
identical 



188 




l 

fc^^fc 



Fig. 137. From a distance 

the circular white spots 

seem hexagonal 



Fig. 138. From a distance the black 
dots appear as hexagons 



on a white background (Fig. 138) also seem hexagonal from far away, 
though irradiation does not enlarge, but, on the contrary, reduces 
the dots in size. One must note that the explanations afforded for optic- 
al illusions in general are not completely satisfactory. As a matter 
of fact, most illusions still have to be explained. (For more on the topic 
see my Optical Illusions album.) 



WHICH IS BLACKER? 

Fig. 1S9 introduces us to another imperfection of the eye "astig- 
matism" this time. Look at it with one eye. Not all four letters will 
seem identical in blackness. Note which is the blackest and turn the 
drawing sideways. The letter you thought the blackest will suddenly 
go grey, and now another letter will seem the blackest. Actually, all 




Fig. 139. Look at this word with one eye. One letter 
will seem hlacker than the rest 



four letters are identical in blackness; they are merely shaded in differ- 
ent directions. If our eyes were just as perfect and faultless as expen- 
sive glass lenses, this would have no effect on the blackness of the 
letters; but since our eyes do not refract light identically in differ- 
ent directions, we cannot see vertical, horizontal, and slanting lines 
just as distinctly. 

Very seldom is the eye absolutely free of this shortcoming. With 
some people astigmatism is so great that it noticeably lessens the 
acuteness of vision and they have to wear special glasses to correct this. 
Our eyes also have other imperfections, which opticians know how to 
avoid. This is what Hclmholtz had to say about them: 

"If an optician were to dare sell me an instrument with such imper- 
fections, I would most roundly chide him and demonstratively return 
the instrument." 

Besides these illusions which our eyes succumb to due to certain 
imperfections in them, there are many other illusions to which they 
fall victim for totally different reasons. 



STARING PORTRAIT 

You have most likely seen at one time or another portraits that not 
only look you square in the eye, but even follow you with their eyes 
wherever you go. This was noticed long ago and has always baffled 
many, giving some the jitters. The great Russian writer Nikolai Gogol 
provides a wonderful description of this in his "Portrait": 

"The eyes dug right into him and seemed wanting to watch only him 
and nothing else. The portrait stared right past everything else, straight 
at him and into him." 

Quite a number of superstitions and legends are associated with this 
mysterious stare. Actually it is nothing more than an optical illusion. 
The trick is that on these portraits the pupil is placed square in the 
middle of the eye just as we would see it in the eye of anybody look- 
ing at us point-blank. When a person looks past us, the pupil and the 
entire iris are no longer in the centre of the eye; they shift sideways. 

190 



On the portrait, however, the pupil stays 
right in the centre of the eye which- 
ever way we step. And since we continue 
to see the face in the same position in 
relation to us, we, naturally, think that 
the man in the portrait has turned his 
head our way and is watching us. This 
explains the odd sensation we derive 
from other such pictures the horse 
seems to be charging straight at us how- 
ever hard we try to dodge it; the man's 
finger keeps pointing straight at us, and 
so on and so forth. Fig. 140 is one such 
picture. They are often used to advertise 
or for propaganda purposes. 

MORE OPTICAL ILLUSIONS 




Fig. 140. The mysterious 
portrait 



There doesn't seem to be anything 

out of the ordinary in the set of pins in Fig. 141, does there? However, 
lift the book to eye level and, cupping one eye, look at the pins so 
that your line of vision slides along them, as it were. Your eye must be 
at the point where the imagined continuations of these pins cross. Then 
the pins will seem to be stuck in the paper upright. When you shift 
your head sideways, the pins] seem to sway in the same direction. 

This illusion is governed by laws of perspective. The drawing is of 
upright pins projected on paper as they appear to the observer when 
viewed from the given point. 

Our ability to succumb to optical illusions should not at all be regard- 
ed as just an imperfection of our eyesight. This ability presents a 
definite advantage, often overlooked, which is that without it we would 
have no painting; nor, in general, would we derive any pleasure from 
the fine arts. Artists draw extensively on these imperfections of our 
vision. 

"The whole art of painting is based on this illusion," the brilliant 
18th-century scholar Euler wrote in his famous Letters on Various 



191 




Fig. 141. Fix one eye (have 
the other shut) at the point 
where the imagined continua- 
tions of the pins would con- 
verge. The pins will seem to 
be stuck in the paper upright. 
By gently shifting the hook 
from side to side, you get 
the impression that the pins 
are swaying 



Physical Subjects. "If we passed judgement 
on things by what they really were, this 
art (painting) could not exist and we would 
be blind. The painter would strive in vain 
to mix his colours, for we would say 
here is red and there is blue, here is black 
and there are dashes of white. Everything 
would be contained in one plane; no differ- 
ence in distance would be observed and 
no object could be depicted. Whatever the 
painter would want to show would all seem 
to us as writing on paper. And given this 
perfection, would we not be deserving of 
pity on being robbed of the delight such 
p leasant and useful artistry affords us daily? " 
There are very many optical illusions, 
enough (to fill albums (the Optical Illu- 
sions album mentioned earlier contains 
more than sixty). Many are common, oth- 
ers are less known. I shall give you some 



of the more curious instances that are less 

known. The illusions provided by Figs. 142 and 143, with lines on 
a checkered background, are particularly effective. One simply can't 
believe that the letters in Fig. 142 are straight and it is still harder 
to believe that the circles in Fig. 143 are not one spiral. The only 
way to check it is L to apply a pencil and trace the circles. Only a pair 
of compasses will tell us that the straight line AC in Fig. 144 is just 
as long as AB and not shorter, as it appears to be. The other illusions 
in Figs. 145, 146, 147, and 148 are explained in the captions. The 
following curious incident shows how effective the illusion Fig. 147 
provides is. When the publisher of a previous edition of this book 
was examining the clich6, he thought it badly done and was about to 
return it to the printshop to have the grey splotches at the intersec- 
tion of the white lines scraped off, when I chanced to intervene and 
explained the matter. 



192 




Fig. 142. The letters are upright 




Fig. 143. This seems a spiral; actually the curves are circles, 
which you can see for yourself by following the lines with a 

pointed pencil 



e 



. c 




Fig. 144. AB is equal to AC, though 
AB seems longer 



M 



Fig. 145. The slanting 
line seems broken 




Fig. 147. Tiny faint grey 
squares seem to appear and 
disappear where the white 
strips cross, though the strips 
arc really white throughout, 
as can be demonstrated by 
closing up the black squares 
with a piece of paper. Tho 
illusion is due to contrasts 




Fig. 140. The white and 

black squares are identical, 

as, too, are the round white 

and black spots 



Fig. 148. Faint grey squares 
seem to appear and disappear 
where the black strips cross 



SHORT-SIGHTED VISION 

With his spectacles off, a short-sighted person sees badly. {But what 
he sees and how he^sees it is something of which people with normal 
eyesight have a very hazy notion. Since many are short-sighted, it would 
not be without interest to learn how they see. 

Firstly, to the short-sighted person everything seems blurred. What 
to a person with normal eyesight are leaves and twigs all clearly 
etched against the sky are to the short-sighted merely an amorphous 
mass of green. He misses the minor details. Human faces seem young- 
er and more attractive; crow's feet and other minor blemishes are not 
seen; the coarse ruddiness that may be the product of nature or make- 
up appears as a delicate flush. He may miscalculate age, being as much 
as 20 years out. He has odd tasteto those with good eyesight of 
the beautiful. He may be considered tactless when he looks a person 
straight in the eye but seems reluctant to recognise him. He is not to 
blame. It is his near-sightedness that is the culprit. 

"At the Lycee," the 19th-century Russian poet Delvig wrote, 
"I was forbidden to wear spectacles and my female acquaintances 
seemed exquisite creatures. How shocked I was after graduation!" 
When your short-sighted friend (minus his spectacles) chats with 
you he doesn't see your face, or, at any rate, what you think he sees. 
His image of you is blurred. No wonder he fails to recognise you an hour 
later. Most short-sighted people recognise others not so much by their 
outer appearance as by the sound of their voices. Inadequate vision is 
compensated for by acuter hearing. 

Would you like to know what the near-sighted sees at night? All 
bright objects street lanterns, lamps, lighted windows, etc. assume 
enormous proportions and transform the world around into a chaotic 
jumble of shapeless bright splotches and dark and misty silhouettes. 
Instead of a row of street lamps the short-sighted sees two or three 
huge bright patches, which blot out the rest of the street. He cannot 
make out an approaching motor car; instead he sees just the two bright 
halos of its front lights and a dark mass behind. Even the sky seems 
different. The short-sighted sees stars of only the first three or four 
stellar magnitudes. Consequently, instead of several thousand stars 

195 



he sees only a few hundred, which seem to be as large as lamps. The 
moon seems tremendous and very close, while a crescent moon takes 
on a phantastic form. 

The fault lies in the structure of the eye; the eye-ball is too deep, 
so much so that its changed refractive power causes images from distant 
objects to be focussed before they reach the retina. The blurred retinal 
image is produced by diverging beams of light. 



CHAPTER TEN 

SOUND AND HEARING 

HUNTING THE ECHO 

Mark Twain tolls a vory funny story of the misadventures of a 
man whose hobby was to collect you'll never guess echoes! This 
eccentric spared no effort to buy up every tract of land that would 
have a multiple echo or some other extraordinary natural echo. 

"His first purchase was an echo in Georgia that repeated four times; 
his next was a six-repeater in Maryland; his next was a thirteen-re- 
peater in Maine; his next was a nine-repeater in Kansas; his next was 
a twelve-repeater in Tennessee, which he got cheap, so to speak, because 
it was out of repair, a portion of the crag which reflected it having 
tumbled down. He believed he could repair it at a cost of a few thou- 
sand dollars, and, by increasing the elevation with masonry, treble 
the repeating capacity; but the architect who undertook the job had 
never built an echo before, and so he utterly spoiled this one. Before 
he meddled with it, it used to talk back like a mother-in-law, but now 
it was only fit for the deaf and dumb asylum." 

Joking apart, Ihero are some wonderful discrete multiple echoes 
in various primarily mountainous spots, some of which are of 
long-standing universal fame. The following are some of the bettor- 
known echoes. The Woodstock castle echo in England repeats seventeen 
syllables quite distinctly. The ruins of the Derenburg castle near Hal- 
berstadt echoed 27 syllables before one of its walls was blown up. There 
is one definite place in the rocky cirque near Adersbach in Czechoslo- 
vakia which echoes seven syllables thrice; however, a few steps aside 
even a gunshot will fail to produce any response. There was a castle 
near Milan that had a very fine repeater-echo before it was demolished. 

142668 197 




A shot fired from a window 
in one of its wings echoed 
back 40 to 50 times, and a 
word said in a loud voice, some 
30 times. 

It is not so easy to find 
even a discrete single echo. 
The U.S.S.R. is a bit better 
off in this respect as it has 
many open plains ringed by 
woods and many forest clear- 
ings, where a shout will al- 
ready produce a response in 
the form of a more or less 
distinct echo comirg back 
from the wall of forest. In 
mountain land echoes are more 
varied than in plains, but 
occur much more seldom and 
are harder to catch. Why 

is this so? Because an echo is nothing but a train of sound waves re- 
flected back by some obstacle. Sound abides by the same laws as light: 
its angle of incidence is equal to its angle of reflection. 

Imagine yourself at the foot of a hill (Fig. M9), with the sound* 
reflecting barrier AB higher than you are. Naturally the sound waves 
propagating along the lines Ca> Cb and Cc will not reflect back to your 
ear but into the air along the directions aa, bb and cc. On the other 
hand, when the sound-reflecting barrier is at (he same level with 
you or even a bit lower, as in Fig. 150, you will hear an echo. The sound 
travel? down along Ca and Cb and returns along the broken lines CaaC 
or Cbl)C t bouncing off the ground once or twice. The pocket between 
the points acts like a concave mirror and makes the echo still more 
distinct. Were the ground between the two points C and B a bulge the 
echo would be very faint and might not reach you at all, because it 
would diffuse sound just as a "convex mirror diffuses light. 
You must develop a certain knack to detect an echo on uneven ter- 



Fig. 149. There is no echo 



198 




Fig. 150. There is a distinct echo 

rain, and even then you must also know how to produce it. In the first 
place, don't stand too close to the obstacle. The sound waves must 
travel a long enough distance because otherwise the echo will occur 
too early and merge with the sound it self. Since sound propagates 
with the speed of 310 m/sec, at a distance of 5 metres away the echo 
should be heard exactly half a second later. Though every sound has 
its echo, not every echo is as distinct, depending on whether it is 
a beast roaring in a forest, a bugle blowing, thunder reverberating, 
or a girl singing. The more abrupt and louder the sound, the more 
distinct is the echo. A hand-clap is best. The human voice is less suit- 
able, especially a man's voice. The high-pitched voices of women 
and children furnish a more distinct echo. 

SOUND AS RULER 

Sometimes one can use one's knowledge of the velocity with which 
sound travels in air to measure the distance to an inaccessible object. 
Jules Verne provides a case in point in his Journey to the Centre of 
Earth, where in the course of their subterranean exploration the two 
travellers, the professor and his nephew, lost each other. They hal- 
looed, and when they finally heard each other the following conversa- 
tion took place between them. 

"'Uncle, 1 I [the nephew] spoke. 

"'My boy, 1 was his ready answer. 



M* 



19$ 



"'Jt is of the utmost consequence thai we should know how far we 
are asunder.' 

'"That is not difficult/ 

"'You have your chronometer at hand?' f asked. 

14 'Certainly. 1 ' 

"'Well, take it into your hand. Pronounce iny name, noting exactly 
the second at which you speak. I will reply as soon as I hear your 
words and you will then note exactly the moment- at which my reply 
reaches you.' 

"'Very good; and the mean time between my question and your 
answer will ho the time occupied by my voice in reaching you....' 

"'Are you ready?' 

"'Yes.' 

"'Well, I am about to pronounce your name,' said the professor. 

"I applied my ear close to the sides of the cavernous gallery, and as 
soon as the word 'Harry' reached my ear, 1 turned round and, placing 
my lips to the wall, repeated the sound. 

"'Forty seconds,' said my uncle. 'There has elapsed forty seconds 
between the two words. The sound, therefore, takes twenty seconds 
to travel. Now, allowing a thousand and twenty feet for every second, 
we have twenty thousand four hundred feeta league and a half and 
one-eighth.'" 

Now you should be able to answer this question: How far away is 
the train engine if I hear its toot one and a half seconds after I see the 
wisp of smoke rise from the whistle? 

SOUND MIRRORS 

A forest wall, high fence, building, mountain, or any echo-produc- 
ing obstacle in general is nothing but a sound mirror, as it reflects sound 
in tho same way as an ordinary flat mirror reflects light. 

You can also have a concave sound mirror that would focus the 
wave-trains of sound. With two soup dishes and a watch you can stage 
the following illuminating experiment. Put one dish on the table and 
hold the watch a few centimetres above its bottom. Hold the other 
dish near your ear as shown in Fig. 151. If you gauge the position of 

200 



all three objects right do this by trial and 
error the ticking of the watch will sewn to 
come from the dish near your ear. But shut- 
ting your eyes you enhance the illusion anil 
your ear alone will not loll you in which 
hand you are holding the watch. 

Mediaeval castle-builders often played tricks 
with sound, by placing a bust either at the 
focus of a concave sound mirror or at the tail 
end of a speaking pipe cunningly concealed 
in the wall. Fig. 152, which has boon taken 
from a 16th-century book, shows these arrange- 
ments. The vaulted ceiling reflects to the 
bust's lips all sounds coming in through the 
speaking pipe; tho huge brickcd-in speaking 

pipes carry sounds from the courtyard to the marble busts placed near 
the walls in one of tho galleries, etc. The illusion of whispering or sing- 
ing busts is thus produced. 




757. (Concave" sound 
mirrors 




Fig. H2. Whispering busts (from a hook hy AthamiHiis Kirrhor. 1560) 



SOUND IN THEATRE 

The theatre- and concert-goer knows very well that there are halls 
with good acoustics and bad acoustics. In some speech and music carry 
distinctly tt) quite a distance; in others they are muted even quite 
near. 

Not so long ago the good acoustics of one or another theatre was 
considered simply a stroke of good luck. Now builders have found 
ways and means of successfully suppressing objectionable reverbera- 
tion. Though I shall not expand on this point as it can interest only 
the architect, let me note that the main way of avoiding acoustical 
defects is to create surfaces to absorb superfluous sounds. 

An open window absorbs sound best just as any aperture is best 
for absorbing light. Incidentally, a square metre of opon window has 
been accepted as the standard unit to estimate sound absorption. 
The audience itself is a good sound-absorber, with every person being 
equivalent to roughly half a square metre of open window. "The aud ience 
literally absorbs what the speaker snys," one physicist said; it is just 
as true that the absence of an absorbing audience is literally a great 
annoyance for a speaker. 

When too much sound is absorbed, this is also bad, as, firstly, it 
mutes speech and music, and, secondly, suppresses reverberation so 
much that the sounds seem ragged and brittle. As we see, some meas- 
ureneither too long, nor too shortof reverberation is desirable. 
This measure cannot be the same for all halls and must be quantita- 
tively estimated by the designing architect. 

There is another place in the theatre of interest from the angle of 
physics. This is the prompt box. It always has the same shape have 
you ever noticed that? Physics is responsible. Its ceiling a concave 
sound mirror serves a dual purpose: firstly, to prevent what the 
prompter is saying from reaching the aud ience, and , secondly, to reflect 
his voice towards the actors on the stage. 

SEA-BOTTOM ECHO 

Echoes wfcre useless until a method was devised to sound sea and 
ocean depths with their help. We stumbled upon this invention by 
accident. When in 1912 the huge ocean liner Titanic ran afoul of 

202 




an iceberg and went down with nearly all its passengers, navigators 
thought of employing the echo during fogs or at night to detect ob- 
stacles in a ship's way. Though this failed to achieve its original pur- 
pose, it suggested a fine method, whereby sea depths could be sounded 
by the echo from the sea-bottom. 

Fig. 153 shows you how this is done. 
By igniting a detonator against the ship's 
skin near the keel a sharp signal is sent. 
The sound pierces the water, reaches 
the sea-bottom and echoes back. This 
echo, the reflected signal, is recorded 
by a sensitive device placed against the 
ship's skin. An accurate timepiece gauges 
the time interval between the send- 
ing of the signal and the reception of 
the echo. Knowing how fast sound trav- 
els in water, we can easily reckon the 
distance to the reflecting barrier, or, in 
other words, ascertain the depth. 

Echo depth-sounding completely revo- 
lutionised sounding practices. To use 
the old methods one had to stop the ship; 
and, in general, they were a very tedious 
affair. The line was payed out very 
slowly at the rate of 150 metres a minute 
and it took the same amount of time 
to rewind it. For instance, it took about 
45 minutes to sound a depth of three 
kilometres. Echo sounding produces 
the same result in but a few seconds. Furthermore, we don't have 
to stop the ship to do it and the result is incomparably more 
accurate, being never more than a quarter of a metre out provided 
the time is gauged with an accuracy down to the three-thousandths 
of a second. 

Whereas the exact sounding of great depths is important for 
oceanography, the quick, reliable and accurate ascertainment of 



Fig. 



153. Echo 
sounding 



depth- 



203 



shallow depths is essential for safe steering, especially in offshore 
waters. 

To take soundings today, people employ not ordinary sounds but 
extremely intensive "ultra-sounds", which we will never hear as their 
frequency ranges into several million vibrations a second. These sounds 
are produced by the vibrations of a quartz plate (a piezo-quartz) which 
is placed in a quickly alternating electric field. 

WHY DO BEES BUZZ? 

Indeed, why? After all most insects have no special organ for the 
purpose. The buzzing, which is heard only while the insect is flying, 
is produced by the flapping of the insect's wings, which vibrate with 
a rapidity of several hundred times a second. The wings act the role 
of a vibrating plate, and any plate vibrating with sufficiently great 
rapidity more than 16 times a second produces a tone of a definite 
pitch. 

It is this that reveals to scientists how many times a second an in- 
sect moves its wings in flight. To determine the number of times, it 
is enough to ascertain the pitch of the insect's buzzing, because each 
tone has its own vibration frequency. With the aid of the slow-motion 
camera (mentioned in Chapter One) scientists proved that each insect 
vibrates its wings with practically the same rapidity on every occasion; 
to regulate its flight it modifies only the "amplitude" of its wing move- 
ment and the angle at which the wing is inclined; it increases the 
number of wing movements per second only in cold weather. That 
is why the tone of the buzz remains on one level. The ordinary 
house fly, for instance its buzz gives the tone F vibrates its 
wings 352 times a second. The bumblebee moves its wings 220 times. 
A honey bee vibrates its wings 440 times a second (tone A) when 
not burdened with honey, and only 330 times (tone B) when carrying 
it. Beetles, whose buzzing is lower-pitched, move their wings much 
less nimbly. Mosquitoes, on the other hand, vibrate their wings 
between 500 and 600 times a second. Let me note for the sake of 
comparison that an airplane propeller averages only some 25 revo- 
lutions a second. 

204 



AUDITORY ILLUSIONS 

Once we for some reason imagine the source of a slight noise to be 
far away, the noise will seem much louder. We frequently succumb to 
these illusions but rarely pay any heed to them. The following cur- 
ious instance was described by the American scientist William James 
in his Psychology* 

"Sitting reading, late one night, I suddenly heard a most formidable 
noise proceeding from the upper part of the house, which it seemed 
to fill. It ceased, and in a moment renewed itself. I went into the hall 
to listen, but it came no more. Resuming my seat in the room, how- 
ever, there it was again, low, mighty, alarming, like a rising flood or 
the avant-courier of an awful gale. It came from all space. Quite startled, 
I again went into the hall, but it had already ceased once more. 
On returning a second time to the room, I discovered that it was nothing 
but the breathing of a little Scotch terrier which lay asleep on the 
floor. The noteworthy thing is that as soon as I recognised what 
it was, I was compelled to think it a different sound, and could not 
then hear it as I had heard it a moment before. " Has anything of the 
sort ever happened to you? Most likely it has; I, for one, have observed 
such things more than once. 

WHERE'S THE GRASSHOPPER? 

We very often err in determining not how far away the sound is, 
but the direction from which it comes. We can distinguish pretty well 
by ear whether the shot was fired to the right or left of us (Fig. 154), 
but we are often unable to determine whether it was fired in front of 
us or behind us (Fig. 155). We often hear a shot fired in front of us as 
one coming from behind. All we can say in such cases is whether it 
is near or far depending on how loud the shot is. 

Here is a very instructive experiment. Blindfold your friend and 
seat him in the middle of a room. Ask him to sit still and not turn his 
head. Then take two coins and click them against each other, standing 
meanwhile in the imagined vertical plane that passes between your 
friend 's eyes, and ask him to guess where the sound was made. Sur- 
prisingly enough, ho will point anywhere except at you. But as soon 

205 




754. Where was the shot fired? On the right or on the left? 



Fig. US. 

W here was 

the shot fired? 

In front? 

Or behind? 



as you leave that plane of symmetry which I men- 
tioned, his guessing will be much better, because his 
ear closest to you will bear the sound a bit earJier 
and a bit louder. 

This experiment, incidentally, explains why it is 
so difficult to spot a chirring grasshopper. You hear 
this shrill singing some two steps away on your right. 
You turn your head but see nothing, and now hear the grasshopper 
on your left. Again you turn your head, only to hear the singing 
come from some other spot. The quicker you turn your head, the 
nimbler our invisible musician see ins. Actually, the grasshopper 
hasn't moved; you've only imagined it to be hopping about. You 
have fallen victim to an auditory illusion. 

Your mistake is that you turn your head so that the grasshopper 
occupies its symmetrical plane. As you already know, this readily 



206 



causes you to blunder in determining the direction. So, if you want to 
find the grasshopper, the cuckoo, or any other similar distant source 
of sound, turn your head not in the direction from which it comes but 
away from it, which, incidentally, is exactly what one does when 
one "pricks up one's ears'*. 

THE TRICKS OUR EARS PLAY 

When we nibble at a rusk we hear a noise that is simply deafening. 
But for some reason our neighbour makes hardly any noise though 
he is doing the same. How come? The noise we make is one that only 
we ourselves can hear and it doosn't annoy our neighbours. The point 
is that like all solid elastic bodies, the bones of our head are very good 
conductors of sound. The denser the medium through which sound 
travels, the louder it is. The sound our neighbour makes when nib- 
bling a rusk is a very light one as it travels through air, but this same 
sound turns into thunder when it reaches the auditory nerve via the 
solid bones of your head. 

Do the following. Grip the strap-ring of your pocket watch be- 
tween your teeth and stop up your ears. The bones of your head will 
amplify the ticking so greatly that you seem to hear the pounding of 
heavy hammers. 

The deaf Beethoven, the story goes, could hear a piano being played 
by placing one end of his walking stick on il and gripping the other end 
between his tooth. In the same way deaf people can dance to music, 
provided there is nothing wrong with their internal ear. The music 
reaches the auditory nerve via the floor and the bones of the head. 

Ventriloquism and the "marvels" it works are all based on the 
peculiar properties of hearing that have just been described. 

The illusion that ventriloquism produces depends wholly on our ina- 
bility to determine both where the voice is coming from and how far 
away it is. Ordinarily we can do this only approximately. As soon as 
we find ourselves in unusual circumstances we already make the crudest 
of blunders in trying to say where the sound comes from. I, too, couldn't 
rid myself of the illusion when I was listening to a ventriloquist, even 
though I very well knew what the matter was. 

207 



99 QUESTIONS 

1. How much slower is a snail than you are? 

2. How fast do modern aircraft fly? 

3. Can you overtake the Sun? 

4. How do we get slow-motion films? 

5. When do we move round the Sun faster? 

6. Why are the upper spokes of a rolling wheel blurred and the 
lower spokes seen distinctly? 

7. Which points in a train going forward move backwards? 

8. What is aberration of light? 

9. Why do we lean forwards or shove our feet under a chair whon 
we get up? 

10* Why does a sailor waddle? 

11. What is the difference between running and walking? 

12. How should one jump off a moving car? Explain. 

13. Baron Munchausen, that famous teller of "tall stories", claimed 
he had caught flying cannon balls with his hands. Gould he have done 
that? 

14. Would you like to have presents tossed at you when you're driv- 
ing a car? 

15. Does a body weigh more or less when falling than when at rest? 

16. Must everything fall back to Earth? 

17. Is Jules Verne's description of life inside the projectile, thai 
set off for the Moon, right? 

18- Can you weigh things right on faulty scales with correct weights, 
or on a properly calibrated balance, but with wrong weights? 

19. Are the bones of our arm advantageous levers? 

20. Why doesn't a skier sink into soft snow? 

21. Why is it pleasant to loaf in a hammock? 

22. How was Paris shelled in the First World War? 
23- Why does a kite fly? 

24. Does a stone continue accelerating all the time it drops? 

25. What is the greatest speed a parachutist making a delayed jump 
can achieve? 

26. Why does a boomerang boomerang? 

208 



27. Can we find out whether an egg is boiled without cracking it 
open? 

28. Where is a thing heavier? Closer to the equator or to the poles? 

29. When a seed germinates on the rim of a spinning wheel, in which 
direction does it stem? 

30. What is perpetuum mobile? 

31. Has a "perpetual motion" machine over been made? 

32. Where does a body immersed in a liquid experience the greatest 
pressure? From the top, the sides, or the bottom? 

33. What happens when a small weight suspended on a piece of thread 
is dipped into a jar of water balanced on a pair of scales? 

34. What shape does liquid take when it weighs nothing? Can you 
prove this experimentally? 

35. Why are raindrops round? 

36. Is it true that kerosene oozes through glass or metal? Why do 
people think it does? 

37. Can you make a steel needle float? 

38. What is notation? 

39. Why does soap wash dirt off? 

40. Why does a soap bubble rise? And where does it rise fasterin 
a cold or warm room? 

41. What is thinner? The human hair or the film of a soap bubble? 
How many times is one thinner than the other? 

42. Water gathers under a glass when it's placed, with a burning 
piece of paper in it, bottom up on a tray of water. Why does this happen? 

43. Why does a liquid rise when sipped through a straw? 

44. A stick is balanced by weights on a pair of scales. Will the equi- 
librium be disturbed if the scales are placed under an evacuated bell? 

45. What happens to these scales if placed in liquified air? 

46. If you lost your weight, but your clothes didn't, would you fly 
up into the air? 

47. What difference is there between a "perpetual motion" machine 
and a "gift-power" machine? Have any "gift-power" machines been 
made? 

48. What happens to tram rails on a very hot day or on a very cold 
one? And why is the weather not so dangerous for railway tracks? 

209 



49. When do telegraph and telephone wires sag most? 

50. What sort of tumblers crack more often because of hot or cold 
water? 

51. Why do lemonade glasses have a thick bottom and why are 
they no good as tea glasses? 

52. What sort of transparent material that wouldn't crack because 
of heat or cold is best for tableware? 

53. Why is it hard to draw a boot on after a hot bath? 

54. Can we make a self-winding clock? 

55. Can the self-winding principle be used for bigger machines? 

56. Why does smoke curl up? 

57. What would you do if you wanted to ice a bottle of lemonade? 

58. Will ice melt sooner if wrapped in fur? 

59. Is it true that the snow warms the Earth? 

60. Why doesn't water freeze in underground pipes in winter? 

61. Where is it winter in the Northern Hemisphere in July? 

62. Why can you boil water in a welded vessel, without fearing that 
it might come to pieces? 

63. Why does a sled cross snow with difficulty in a heavy frost? 

64. When can we roll good snowballs? 

65. How do icicles form? 

66. Why is it warmer at the equator than at the poles? 

67. When would we see the Sun rise if light propagated instanta- 
neously? 

68. What would happen to telescopes and microscopes if light propa- 
gated instantaneously in any medium? 

69. Can we make light circumvent obstacles? 

70. How is a periscope made? 

71. Where should you place a lamp to see yourself better in a mirror? 

72. Are you and your reflection in a mirror completely identical? 

73. Is the kaleidoscope of any benefit? 

74. How can we use ice to light a fire? 

75. Can you see mirages in the temperate zones? 

76. What is the "green ray"? 

77. How should one look at photographs? 

210 



78. Why do photographs acquire relief and depth when looked at 
through a magnifying glass or in a concave mirror? 

79. Why is it best to seat oneself in the middle of a movie-house? 

80. Why is it better to look at a painting with one eye? 

81. How does a stereoscope work? 

82. How can we see things like the giants in fairy tales? 

83. What is a telcstercoscope? 

84. Why do things sparkle? 

85. Why does the landscape acquire deeper relief when viewed from 
a passing train? 

86. How are stereoscopic photographs of celestial objects taken? 

87. What is the effect of the so-called "shadow marvel" based on? 

88. What colour does a red flag assume in blue light? 

89. What is irradiation and astigmatism? 

90. What kind of pictures follow you with their eyes? And why? 

91. Is it a person with normal eyesight or a short-sighted person 
who thinks the bright stars bigger? 

92. When you hear the echo 1.5 seconds after you clap your hands, 
how far away is the sound barrier? 

93. Are there such things as sound mirrors? 

94. Where does sound propagate faster, in air or in water? 

95. To what technical uses can echoes be put? 

96. Why does a bee buzz? 

97. Why is it so hard to spot a chirring grasshopper? 

98. What transmits sound better air or some denser medium? 

99. What is ventriloquism based upon? 



There is a second part to this book. However, both can be read inde- 
pendently of each other. 



51. OEPEJlbMAH 

3AHHMATEJIbHAfl OH3HKA 

KHHTB I 



Printed in the Union of Soviet Socialist Republics